Bartleby Sitemap - Textbook Solutions
All Textbook Solutions for Finite Mathematics for Business, Economics, Life Sciences and Social Sciences
In Problems 13-24, find rational number representations for each, if they exist. 82/3In Problems 25-34, simplify each expression and write answers using positive exponents only. All variables represent positive real numbers. x4/5x2/5In Problems 25-34, simplify each expression and write answers using positive exponents only. All variables represent positive real numbers. y3/7y4/7In Problems 25-34, simplify each expression and write answers using positive exponents only. All variables represent positive real numbers. m2/3m1/3In Problems 25-34, simplify each expression and write answers using positive exponents only. All variables represent positive real numbers. x1/4x3/4In Problems 25-34, simplify each expression and write answers using positive exponents only. All variables represent positive real numbers. 8x3y61/3In Problems 25-34, simplify each expression and write answers using positive exponents only. All variables represent positive real numbers. 4u2v41/2In Problems 25-34, simplify each expression and write answers using positive exponents only. All variables represent positive real numbers. 4x2y41/2In Problems 25-34, simplify each expression and write answers using positive exponents only. All variables represent positive real numbers. w49x21/2In Problems 25-34, simplify each expression and write answers using positive exponents only. All variables represent positive real numbers. 8x1/3121/4In Problems 25-34, simplify each expression and write answers using positive exponents only. All variables represent positive real numbers. 6a3/415a1/3Simplify each expression in Problems 35-40 using properties of radicals. All variables represent positive real numbers. 2x+35536ESimplify each expression in Problems 35-40 using properties of radicals. All variables represent positive real numbers. 6x15x330x7Simplify each expression in Problems 35-40 using properties of radicals. All variables represent positive real numbers. 16a454a258a35Simplify each expression in Problems 35-40 using properties of radicals. All variables represent positive real numbers. 6x1015x40EIn Problems 41-48, multiply, and express answers using positive exponents only. 3x3/44x1/42x8In Problems 41-48, multiply, and express answers using positive exponents only. 2m1/3(3m2/3m6)In Problems 41-48, multiply, and express answers using positive exponents only. 3u1/2v1/2u1/24v1/2In Problems 41-48, multiply, and express answers using positive exponents only. a1/2+2b1/2a1/23b1/2In Problems 41-48, multiply, and express answers using positive exponents only. 6m1/2+n1/26mn1/2In Problems 41-48, multiply, and express answers using positive exponents only. 2x3y1/32x1/3+1In Problems 41-48, multiply, and express answers using positive exponents only. 3x1/2y1/22In Problems 41-48, multiply, and express answers using positive exponents only. x1/2+2y1/22Write each expression in Problems 49-54 in the form axp+bxq. where a and b are real numbers and p and q are rational numbers. x23+22x3Write each expression in Problems 49-54 in the form axp+bxq. where a and b are real numbers and p and q are rational numbers. 12x34xWrite each expression in Problems 49-54 in the form axp+bxq. where a and b are real numbers and p and q are rational numbers. 2x34+x33xWrite each expression in Problems 49-54 in the form axp+bxq. where a and b are real numbers and p and q are rational numbers. 3x23+x5xWrite each expression in Problems 49-54 in the form axp+bxq. where a and b are real numbers and p and q are rational numbers. 2x3x4xWrite each expression in Problems 49-54 in the form axp+bxq. where a and b are real numbers and p and q are rational numbers. x24x2x3Rationalize the denominators in Problems 55-60. 12mm23mmRationalize the denominators in Problems 55-60. 14x27xRationalize the denominators in Problems 55-60. 2x+3x2Rationalize the denominators in Problems 55-60. 3x+1x+4Rationalize the denominators in Problems 55-60. 7xy2xyRationalize the denominators in Problems 55-60. 3a3ba+bRationalize the numerators in Problems 61-66. 5xy5x2y2Rationalize the numerators in Problems 61-66. 3mm3mmRationalize the numerators in Problems 61-66. x+hxhRationalize the numerators in Problems 61-66. 2a+h2ahRationalize the numerators in Problems 61-66. txt2x2Rationalize the numerators in Problems 61-66. xyx+yProblems 67-70 illustrate common errors involving rational exponents. In each case, find numerical examples that show that the left side is not always equal to the right side. x+y1/2x1/2+y1/2Problems 67-70 illustrate common errors involving rational exponents. In each case, find numerical examples that show that the left side is not always equal to the right side. x3+y31/3x+yProblems 67-70 illustrate common errors involving rational exponents. In each case, find numerical examples that show that the left side is not always equal to the right side. x+y1/31x+y3Problems 67-70 illustrate common errors involving rational exponents. In each case, find numerical examples that show that the left side is not always equal to the right side. x+y1/21x+y2In Problems 71-82, discuss the validity of each statement. If the statement is true, explain why. If not, give a counterexample. x2=x for all real numbers xIn Problems 71-82, discuss the validity of each statement. If the statement is true, explain why. If not, give a counterexample. x2=x for all real numbers xIn Problems 71-82, discuss the validity of each statement. If the statement is true, explain why. If not, give a counterexample. x33=x for all real numbers xIn Problems 71-82, discuss the validity of each statement. If the statement is true, explain why. If not, give a counterexample. x33=x for all real numbers xIn Problems 71-82, discuss the validity of each statement. If the statement is true, explain why. If not, give a counterexample. If r0, then r has no cube roots.In Problems 71-82, discuss the validity of each statement. If the statement is true, explain why. If not, give a counterexample. If r0, then r has no square roots.In Problems 71-82, discuss the validity of each statement. If the statement is true, explain why. If not, give a counterexample. If r0, then r has two square roots.In Problems 71-82, discuss the validity of each statement. If the statement is true, explain why. If not, give a counterexample. If r0, then r has three cube roots.In Problems 71-82, discuss the validity of each statement. If the statement is true, explain why. If not, give a counterexample. The fourth roots of 100 are 10 and 10.In Problems 71-82, discuss the validity of each statement. If the statement is true, explain why. If not, give a counterexample. The square roots of 265 are 32 and 23.In Problems 71-82, discuss the validity of each statement. If the statement is true, explain why. If not, give a counterexample. 3556035=5765In Problems 71-82, discuss the validity of each statement. If the statement is true, explain why. If not, give a counterexample. 7523=12In Problems 83-88, simplify by writing each expression as a simple or single fraction reduced to lowest terms and without negative exponents. 12x2x+33/2+x+31/2In Problems 83-88, simplify by writing each expression as a simple or single fraction reduced to lowest terms and without negative exponents. 2x21/2122x+3x23/2In Problems 83-88, simplify by writing each expression as a simple or single fraction reduced to lowest terms and without negative exponents. x11/2x12x11/2x1In Problems 83-88, simplify by writing each expression as a simple or single fraction reduced to lowest terms and without negative exponents. 2x11/2x+2122x11/222x1In Problems 83-88, simplify' by writing each expression as a simple or single fraction reduced to lowest terms and without negative exponents. x+22/3x23x+21/3x+24/3In Problems 83-88, simplify' by writing each expression as a simple or single fraction reduced to lowest terms and without negative exponents. 23x11/32x+1133x12/333x12/3In Problems 89-94, evaluate using a calculator. (Refer to the instruction book for your calculator to see how exponential forms are evaluated.) 223/2In Problems 89-94, evaluate using a calculator. (Refer to the instruction book for your calculator to see how exponential forms are evaluated.) 155/4In Problems 89-94, evaluate using a calculator. (Refer to the instruction book for your calculator to see how exponential forms are evaluated.) 8273/8In Problems 89-94, evaluate using a calculator. (Refer to the instruction book for your calculator to see how exponential forms are evaluated.) 1033/4In Problems 89-94, evaluate using a calculator. (Refer to the instruction book for your calculator to see how exponential forms are evaluated.) 37.097/3In Problems 89-94, evaluate using a calculator. (Refer to the instruction book for your calculator to see how exponential forms are evaluated.) 2.8768/5In Problems 95 and 96, evaluate each expression on a calculator and determine which pairs have the same value. Verify these results algebraically. (A)3+5(B)2+3+23(C)1+3(D)10+633(E)8+60(F)6In Problems 95 and 96, evaluate each expression on a calculator and determine which pairs have the same value. Verify these results algebraically. (A)22+53(B)8(C)3+7(D)3+8+38(E)10+84(F)1+5Use the square-root property to solve each equation. (A)x26=0(B)3x212=0(C)x2+4=0(D)x+52=1Solve by factoring using integer coefficients, if possible. (A)2x2+4x30=0(B)2x2=3x(C)2x28x+3=0Solve 2x24x3=0 using the quadratic formula.Factor, if possible, using integer coefficients. (A)3x228x464(B)9x2+320x144Find all real solutions to 6x5+192=0.Repeat Example 6 if near the end of summer, the supply and-demand equations are p=x80120suppyequation p=1,264xDemandequationSolve Problems 1-4 by the square-root method. 2x222=0Solve Problems 1-4 by the square-root method. 3m221=0Solve Problems 1-4 by the square-root method. 3x12=25Solve Problems 1-4 by the square-root method. 2x+12=16Solve Problems 5-8 by factoring. 2u28u24=0Solve Problems 5-8 by factoring. 3x218x+15=0Solve Problems 5-8 by factoring. x2=2xSolve Problems 5-8 by factoring. n2=3nSolve Problems 9-12 by using the quadratic formula. x26x3=0Solve Problems 9-12 by using the quadratic formula. m2+8m+3=0Solve Problems 9-12 by using the quadratic formula. 3u2+12u+6=0Solve Problems 9-12 by using the quadratic formula. 2x220x6=013ESolve Problems 13-30 by using any method. x2=34x15ESolve Problems 13-30 by using any method. 9y225=017E18E19E20E21E22ESolve Problems 13-30 by using any method. y24y=824E25E26E27E28E29E30EIn Problems 31-38, factor, if possible, as the product of two first degree polynomials with integer coefficients. Use the quadratic formula and the factor theorem. x2+40x84In Problems 31-38, factor, if possible, as the product of two first degree polynomials with integer coefficients. Use the quadratic formula and the factor theorem. x228x128In Problems 31-38, factor, if possible, as the product of two first degree polynomials with integer coefficients. Use the quadratic formula and the factor theorem. x232x+144In Problems 31-38, factor, if possible, as the product of two first degree polynomials with integer coefficients. Use the quadratic formula and the factor theorem. x2+52x+208In Problems 31-38, factor, if possible, as the product of two first degree polynomials with integer coefficients. Use the quadratic formula and the factor theorem. 2x2+15x108In Problems 31-38, factor, if possible, as the product of two first degree polynomials with integer coefficients. Use the quadratic formula and the factor theorem. 3x232x140In Problems 31-38, factor, if possible, as the product of two first degree polynomials with integer coefficients. Use the quadratic formula and the factor theorem. 4x2+241x434In Problems 31-38, factor, if possible, as the product of two first degree polynomials with integer coefficients. Use the quadratic formula and the factor theorem. 6x2427x360Solve A=P1+r2 for r in terms of A and P : that is, isolate r on the left side of the equation (with coefficient 1) and end up with an algebraic expression on the right side involving A and P but not r. Write the answer using positive square roots only.Solve x2+3mx3mx3n=0 for x in terms of m and nIn Problems 43-48, find all real solutions. x3+8=0In Problems 43-48, find all real solutions. x38=0In Problems 43-48, find all real solutions. 5x4500=0In Problems 43-48, find all real solutions. 2x3+250=0In Problems 43-48, find all real solutions. x48x2+15=0In Problems 43-48, find all real solutions. x412x2+32=0Supply and demand. A company wholesales shampoo in a particular city. Their marketing research department established the following weekly supply-and-demand equations: p=x450+12Supplyequation p=6,300xDemandequationSupply and demand. An importer sells an automatic camera to outlets in a large city. During the summer, the weekly supply-and-demand equations are p=x6+9Supplyequation p=24,840xDemandequation How many units are required for supply to equal demand? At what price will supply equal demand?Interest rate. If P dollars are invested at 100r percent compounded annually, at the end of 2 years it will grow to A=P1+r2. At what interest rate will $484 grow to $625 in 2 years? (Note: If A=625 and P=484, find r.)Interest rate. Using the formula in Problem 51, determine the interest rate that will make $1,000 grow to $1,210 in 2 years.Ecology. To measure the velocity v (in feet per second) of a stream, we position a hollow L-shaped tube with one end under the water pointing upstream and the other end pointing straight up a couple of feet out of the water. The water will then be pushed up the tube a certain distance h (in feet) above the surface of the stream. Physicists have shown that v2=64h. Approximately how fast is a stream flowing if h=1 foot? If h=0.5 foot?Safety research. It is of considerable importance to know the least number of feet d in which a car can be stopped, including reaction time of the driver, at various speeds v (in miles per hour). Safety research has produced the formula d=0.044v2+1.1v . If it took a car 550 feet to stop, estimate the car’s speed at the moment the stopping process was started.Write the first four terms of each sequence: (a) an=-n+3 (b) 1n2nFind the general term of a sequence whose first four terms are (a) 3,6,9,12, (b) 1,2,4,8,Write k=15k+11 Without summation notion. Do not evaluate the sum.Write the alternating series 113+19127+181 using summation notation with (A) The summing index k starting at 1 (B) The summing index j starting at -Find the arithmetic mean of 9,3,8,4,3, and 6.Write the first four terms for each sequence in Problems 1-6. an=2n+3Write the first four terms for each sequence in Problems 1-6. an=4n3Write the first four terms for each sequence in Problems 1-6. an=n+2n+1Write the first four terms for each sequence in Problems 1-6. an=2n+12nWrite the first four terms for each sequence in Problems 1-6. an=3n+1Write the first four terms for each sequence in Problems 1-6. an=14n1Write the 10th term of the sequence in Problem 1.Write the 15th term of the sequence in Problem 2.Write the 99th term of the sequence in Problem 3.Write the 200th term of the sequence in Problem 4.In Problems 11-16, write each series in expanded form without summation notation, and evaluate. k=16kIn Problems 11-16, write each series in expanded form without summation notation, and evaluate. k=15k2In Problems 11-16, write each series in expanded form without summation notation, and evaluate. k=472k3In Problems 11-16, write each series in expanded form without summation notation, and evaluate. k=042kIn Problems 11-16, write each series in expanded form without summation notation, and evaluate. k=13110kIn Problems 11-16, write each series in expanded form without summation notation, and evaluate. k=1412kFind the arithmetic mean of each list of numbers in Problems 17-20. 5,4,2,1,and6Find the arithmetic mean of each list of numbers in Problems 17-20. 7,9,9,2,and4Find the arithmetic mean of each list of numbers in Problems 17-20. 96,65,82,74,91,88,87,91,77,and74Find the arithmetic mean of each list of numbers in Problems 17-20. 100,62,95,91,82.87,70,75,87,and82Write the first five terms of each sequence in Problems 21-26. an=1n+12nWrite the first five terms of each sequence in Problems 21-26. an=1nn12Write the first five terms of each sequence in Problems 21-26. an=n1+1nWrite the first five terms of each sequence in Problems 21-26. an=11nnWrite the first five terms of each sequence in Problems 21-26. an=32n1Write the first five terms of each sequence in Problems 21-26. an=12n+1In Problems 27-42, find the general term of a sequence whose first four terms agree with the given terms. 2,1,0,1,In Problems 27-42, find the general term of a sequence whose first four terms agree with the given terms. 4,5,6,7,In Problems 27-42, find the general term of a sequence whose first four terms agree with the given terms. 4,8,12,16,In Problems 27-42, find the general term of a sequence whose first four terms agree with the given terms. 3,6,9,12,In Problems 27-42, find the general term of a sequence whose first four terms agree with the given terms. 12,34,56,78,In Problems 27-42, find the general term of a sequence whose first four terms agree with the given terms. 12,23,34,45,In Problems 27-42, find the general term of a sequence whose first four terms agree with the given terms. 1,2,3,4,In Problems 27-42, find the general term of a sequence whose first four terms agree with the given terms. 2,4,8,16,In Problems 27-42, find the general term of a sequence whose first four terms agree with the given terms. 1,3,5,7,In Problems 27-42, find the general term of a sequence whose first four terms agree with the given terms. 3,6,9,12,In Problems 27-42, find the general term of a sequence whose first four terms agree with the given terms. 1,25,425,8125,In Problems 27-42, find the general term of a sequence whose first four terms agree with the given terms. 43,169,6427,25681,In Problems 27-42, find the general term of a sequence whose first four terms agree with the given terms. x,x2,x3,x4,In Problems 27-42, find the general term of a sequence whose first four terms agree with the given terms. 1,2x,3x2,4x3,In Problems 27-42, find the general term of a sequence whose first four terms agree with the given terms. x,x3,x5,x7,In Problems 27-42, find the general term of a sequence whose first four terms agree with the given terms. x,x22,x33,x44,Write each series in Problems 43-50 in expanded form without summation notation. Do not evaluate. k=151k+12k12Write each series in Problems 43-50 in expanded form without summation notation. Do not evaluate. k=142k+12k+1Write each series in Problems 43-50 in expanded form without summation notation. Do not evaluate. k=252k2k+3Write each series in Problems 43-50 in expanded form without summation notation. Do not evaluate. k=371kk2kWrite each series in Problems 43-50 in expanded form without summation notation. Do not evaluate. k=15xk1Write each series in Problems 43-50 in expanded form without summation notation. Do not evaluate. k=13xk+1Write each series in Problems 43-50 in expanded form without summation notation. Do not evaluate. k=041kx2k+12k+1Write each series in Problems 43-50 in expanded form without summation notation. Do not evaluate. k=041kx2k2k+2Write each series in Problems 51-54 using summation notation with (A) The summing index k starting at k=1 (B) The summing index j starting at j=0 2+3+4+5+6Write each series in Problems 51-54 using summation notation with (A) The summing index k starting at k=1 (B) The summing index j starting at j=0 12+22+32+42Write each series in Problems 51-54 using summation notation with (A) The summing index k starting at k=1 (B) The summing index j starting at j=0 112+1314Write each series in Problems 51-54 using summation notation with (A) The summing index k starting at k=1 (B) The summing index j starting at j=0 113+1517+19Write each series in Problems 55-58 using summation notation with the summing index k starting at k=1. 2+32+43++n+1nWrite each series in Problems 55-58 using summation notation with the summing index k starting at k=1. 1+122+132++1n2Write each series in Problems 55-58 using summation notation with the summing index k starting at k=1. 1214+18++1n+12nWrite each series in Problems 55-58 using summation notation with the summing index k starting at k=1. 14+9+1n+1n2In Problems 59-62, discuss the validity of each statement. If the r statement is true, explain why. If not, give a counterexample. For each positive integer n, the sum of the series 1+12+13++1n is less than 4.In Problems 59-62, discuss the validity of each statement. If the r statement is true, explain why. If not, give a counterexample. For each positive integer n, the sum of the series 12+14+18++12n is less than 1.In Problems 59-62, discuss the validity of each statement. If the r statement is true, explain why. If not, give a counterexample. For each positive integer n, the sum of the series 12+14+18+1n+12n is greater than or equal to 14.In Problems 59-62, discuss the validity of each statement. If the r statement is true, explain why. If not, give a counterexample. For each positive integer n, the sum of the series 112+13+14+1n+1n is greater than or equal to 12.Some sequences are defined by a recursive formula- that is, a formula that defines each term of the sequence in terms of one or more of the preceding terms. For example, if an is defined by a1=1andan=2an1+1forn2 Then a2=2a1+1=21+1=3 a3=2a2+1=23+1=7 a4=2a3+1=27+1=15 and so on. In Problem 63-66, write the first five terms of each sequence. a1=2andan=3an1+2forn2Some sequences are defined by a recursive formula- that is, a formula that defines each term of the sequence in terms of one or more of the preceding terms. For example, if an is defined by a1=1andan=2an1+1forn2 Then a2=2a1+1=21+1=3 a3=2a2+1=23+1=7 a4=2a3+1=27+1=15 and so on. In Problem 63-66, write the first five terms of each sequence. a1=3andan=2an12forn2Some sequences are defined by a recursive formula- that is, a formula that defines each term of the sequence in terms of one or more of the preceding terms. For example, if an is defined by a1=1andan=2an1+1forn2 Then a2=2a1+1=21+1=3 a3=2a2+1=23+1=7 a4=2a3+1=27+1=15 and so on. In Problem 63-66, write the first five terms of each sequence. a1=1andan=2an1forn2Some sequences are defined by a recursive formula- that is, a formula that defines each term of the sequence in terms of one or more of the preceding terms. For example, if an is defined by a1=1andan=2an1+1forn2 Then a2=2a1+1=21+1=3 a3=2a2+1=23+1=7 a4=2a3+1=27+1=15 and so on. In Problem 63-66, write the first five terms of each sequence. a1=1andan=13an1forn2If A is a positive real number, the terms pf the sequence defined by a1=A2andan=12an1+Aan1forn2 can be used to approximate A to any decimal place accuracy desired. In Problems 67 and 68, compute the first four terms of this sequence for the indicated value of A, and compare the fourth term with the value of A obtained from a calculator. A=2If A is a positive real number, the terms pf the sequence defined by a1=A2andan=12an1+Aan1forn2 can be used to approximate A to any decimal place accuracy desired. In Problems 67 and 68, compute the first four terms of this sequence for the indicated value of A, and compare the fourth term with the value of A obtained from a calculator. A=6The sequence defined recursively by a1=1,a2=1,an=an1+an2forn3 is called the Fibonacci sequence. Find the first ten terms of the Fibonacci sequence.The sequence defined by bn=551+52n is related to the Fibonacci sequence. Find the first ten terms (to three decimal places) of the sequence bn and describe the relationship.Which of the following can be the first four terms of an arithmetic sequence? Of a geometric sequence? (a) 8,2,0.5,0.125, (b) 7,2,3,8, (c) 1,5,25,100,(A) If the 1st and 15th terms of an arithmetic sequence are 5 and 23, respectively, find the 73rd term of the sequence. (B) Find the 8th term of the geometric sequence 164,132,Find the sum of the first 40 terms in the arithmetic sequence: 15,13,11,9,Find the sum of all the odd numbers between 24 and 208.Find the sum of the first eight terms of the geometric sequence: 100,1001.08,1001.082,Repeat Example 6 with a loan of 6,000 over 5 years.Repeat Example 7 with a tax rebate of 2,000.In Problems 1 and 2, determine whether the indicated sequence can be the first three terms of an arithmetic or geometric sequence. and. if so, find the common difference or common ratio and the next two terms of the sequence. (a) 11,16,21, (b) 2,4,8, (c) 5,20,100, (d) 12,16,118,In Problems 1 and 2, determine whether the indicated sequence can be the first three terms of an arithmetic or geometric sequence. and. if so, find the common difference or common ratio and the next two terms of the sequence. (a) 5,20,100, (b) 5,5,5, (c) 7,6,5,6, (d) 512,256,128,In Problems 3-8, determine whether the finite series is arithmetic, geometric, both, or neither. If the series is arithmetic or geometric, find its sum. k=11011k+1In Problems 3-8, determine whether the finite series is arithmetic, geometric, both, or neither. If the series is arithmetic or geometric, find its sum. k=12003In Problems 3-8, determine whether the finite series is arithmetic, geometric, both, or neither. If the series is arithmetic or geometric, find its sum. 1+12+13++150In Problems 3-8, determine whether the finite series is arithmetic, geometric, both, or neither. If the series is arithmetic or geometric, find its sum. 39+27320In Problems 3-8, determine whether the finite series is arithmetic, geometric, both, or neither. If the series is arithmetic or geometric, find its sum. 5+4.9+4.8++0.1In Problems 3-8, determine whether the finite series is arithmetic, geometric, both, or neither. If the series is arithmetic or geometric, find its sum. 114+1911002Let a1,a2,a3,an, be an arithmetic sequence. In Problems 9-14, find the indicated quantities. a1=7;d=4;a2=?;a3=?Let a1,a2,a3,an, be an arithmetic sequence. In Problems 9-14, find the indicated quantities. a1=2;d=3;a2=?;a3=?Let a1,a2,a3,an, be an arithmetic sequence. In Problems 9-14, find the indicated quantities. a1=2;d=4;a21=?;S31=?Let a1,a2,a3,an, be an arithmetic sequence. In Problems 9-14, find the indicated quantities. a1=8;d=75;a15=?S23=?Let a1,a2,a3,an, be an arithmetic sequence. In Problems 9-14, find the indicated quantities. a1=18;a20=75;S20=?Let a1,a2,a3,an, be an arithmetic sequence. In Problems 9-14, find the indicated quantities. a1=203;a30=261;S30=?Let a1,a2,a3,an, be an geometric sequence. In Problems 15-28, find the indicated quantities. a1=3;r=2;a2=?;a3=?;a4=?Let a1,a2,a3,an, be an geometric sequence. In Problems 15-28, find the indicated quantities. a1=32;r=12;a2=?;a3=?;a4=?Let a1,a2,a3,an, be an geometric sequence. In Problems 15-28, find the indicated quantities. a1=1;a7=729;r=3;S7=?Let a1,a2,a3,an, be an geometric sequence. In Problems 15-28, find the indicated quantities. a1=3;a7=2,187;r=3;S7=?Let a1,a2,a3,an, be an geometric sequence. In Problems 15-28, find the indicated quantities. a1=100;r=1.08;a10=?Let a1,a2,a3,an, be an geometric sequence. In Problems 15-28, find the indicated quantities. a1=240;r=1.06;a12=?Let a1,a2,a3,an, be an geometric sequence. In Problems 15-28, find the indicated quantities. a1=100;a9=200;r=?Let a1,a2,a3,an, be an geometric sequence. In Problems 15-28, find the indicated quantities. a1=100;a10=300;r=?Let a1,a2,a3,an, be an geometric sequence. In Problems 15-28, find the indicated quantities. a1=500;r=0.6;S10=?;S=?Let a1,a2,a3,an, be an geometric sequence. In Problems 15-28, find the indicated quantities. a1=8,000;r=0.4;S10=?;S=?Let a1,a2,a3,an, be an geometric sequence. In Problems 15-28, find the indicated quantities. S41=k=183k+3=?Let a1,a2,a3,an, be an geometric sequence. In Problems 15-28, find the indicated quantities. S50=k=1502k3=?Let a1,a2,a3,an, be an geometric sequence. In Problems 15-28, find the indicated quantities. S8=k=182k1=?Let a1,a2,a3,an, be an geometric sequence. In Problems 15-28, find the indicated quantities. S8=k=182k=?Find the sum of the odd integers between 12 and 68Find the sum of all the even integers between 23 and 97Find the sum of each infinite geometric sequence (if it exists) (a) 2,4,8, (b) 2,12,18, 2-Repeat Problem 31 for: (a) 16,4,1, (b) 1,3,9,Find f1+f2+f3++f50 if fx=2x3.Find g1+g2+g3++g100 if gx=183t.Find f1+f2++f10 if fx=12x.Find g1+g2++g10 if gx=2x.Show that the sum of the first n odd positive integers is n2 using appropriate formulas from this section.Show that the sum of the first n even positive integers is n+n2, using formulas in this section.If r=1, neither the first form nor the second form for the sum of a finite geometric series is valid. Find a formula for the sum of a finite geometric series if r=1,If all of the terms of an infinite geometric series are less than 1, could the sum be greater than 1,000 : Explain.Dose there exist a finite arithmetic series with a1=1 and an=1.1 that has sum equal to 100 ? Explain.Dose there exist a finite arithmetic series with a1=1 and an=1.1 that has sum equal to 105 ? Explain.Does there exist an infinite geometric series with a1=10 that has sum equal to 6 ? Explain.Dose there exist an infinite geometric series with a1=10 that has sum equal to 5 ? Explain.Loan repayment. If you borrow $4,800 and repay the loan by paying 200 per month to reduce the loan and 1 of the unpaid balance each month for the use of the money, what is the total cost of the loan over 24 months?Loan repayment. If you borrow $5,400 and repay the loan by paying $300 per month to reduce the loan and 1.5 of the unpaid balance each month for the use of the money, what is the total cost of the loan over 18 months?Economy stimulation. The government, through a subsidy program, distributes $5,000,000. If we assume that each person or agency spends 70 of what is received, and 70 of this is spent, and so on, how much total increase in spending results from this government action? (Let a1=$3,500,000.)Economy stimulation. Due to reduced taxes, a person has an extra $1,200 in spendable income. If we assume that the person spends 65 of this on consumer goods, and the producers of these goods in turn spend 65 on consumer goods, and that this process continues indefinitely, what is the total amount spent (to the nearest dollar) on consumer goods?Compound interest. If $1,000 is invested at 5 compounded annually, the amount A present after n years forms a geometric sequence with common ratio 1+0.05=1.05. Use a geometric sequence formula to find the amount A in the account (to the nearest cent) after 10 years. After 20 years. (Hint: Use a time line.)Compound interest. If $P is invested at 100r compounded annually, the amount A present after n years forms a geometric sequence with common ratio 1+r. Write a formula for the amount present after n years. (Him: Use a time line.)Evaluate. (A)4!(B)7!6!(C)8!5!Find A5C2B6C0Use the binomial theorem to expand x+25.Use the binomial theorem to find the fourth term in the expansion of x220.In Problems 1-20, evaluate each expression. 6!In Problems 1-20, evaluate each expression. 7!In Problems 1-20, evaluate each expression. 10!9!In Problems 1-20, evaluate each expression. 20!19!In Problems 1-20, evaluate each expression. 12!9!In Problems 1-20, evaluate each expression. 10!6!In Problems 1-20, evaluate each expression. 5!2!3!In Problems 1-20, evaluate each expression. 7!3!4!In Problems 1-20, evaluate each expression. 6!5!65!In Problems 1-20, evaluate each expression. 7!4!74!In Problems 1-20, evaluate each expression. 20!3!17!In Problems 1-20, evaluate each expression. 52!50!2!In Problems 1-20, evaluate each expression. 5C3In Problems 1-20, evaluate each expression. 7C3In Problems 1-20, evaluate each expression. 6C5In Problems 1-20, evaluate each expression. 7C4In Problems 1-20, evaluate each expression. 5C0In Problems 1-20, evaluate each expression. 5C5In Problems 1-20, evaluate each expression. 18C15In Problems 1-20, evaluate each expression. 18C3Expand each expression in Problems 21-26 using the binomial theorem. a+b4Expand each expression in Problems 21-26 using the binomial theorem. m+n5Expand each expression in Problems 21-26 using the binomial theorem. x+16Expand each expression in Problems 21-26 using the binomial theorem. u25Expand each expression in Problems 21-26 using the binomial theorem. 2ab5Expand each expression in Problems 21-26 using the binomial theorem. x+2y5Find the indicated term in each expansion in Problems 27-32. x118;5thtermFind the indicated term in each expansion in Problems 27-32. x320;3rdtermFind the indicated term in each expansion in Problems 27-32. p+q15;7thtermFind the indicated term in each expansion in Problems 27-32. p+q15;13thtermFind the indicated term in each expansion in Problems 27-32. 2x+y12;11thtermFind the indicated term in each expansion in Problems 27-32. 2x+y12;3rdtermShow that nC0=nCnforn0.