A Geometric Progression has the following terms: 5000, 5550, ... . Which term in this sequence would first exceed or equal 31,000?  What is the sum from the 1st term to this term?

Q: The first term of an arithmetic sequence is 5. The third term of the sequence is 13. Which of the…

A: Given,First term of AP = a = 5Third term of AP= 13Let, Second term of AP = xWe can write AP as - 5,…

Q: The second term of an infinite geometric progression (|q|<1) is 21 and the sum of the progression…

A: Let the first term= a and common ratio=r  Given the second term= 21 So, ar=21

Q: 4. Find the common difference of the arithmetic sequence for which the first term is -12 and 23rd…

A:

Q: Which one of the following sequences is an arithmetic progression? 3,6,12,24,48,... O 1,4,9,16,25,..…

A:

Q: The second term of a geometric sequence is 6 and the fourth term is 96. Find the possible values of…

A: Since you have posted multiple questions and we can answer one question. So, answered the first…

Q: If the 5th term of a geometric progression is 224 and the 9th term is 3584, then find the 13th term…

A: a5=224⇒ar4=224a9=3584⇒ar8=3584a9a5=ar8ar4=3584224=16r4=16r=2ar4=224a16=224a=22416=14a13=ar12=14×212=…

Q: Use the formula for the sum of the first n terms of a geometric sequence to solve:A pendulum swings…

A: As per the question,                    We are given the geometric sequence which the pendulum…

Q: In a certain geometric sequence, the eighth term is 100 and the common ratio is -(3/2). Find the…

A: Let the first term be a so the sequence will be a, ar, ar2, ar3 ....... The eighth term is 100…

Q: The first term of a geometric sequence is 5. The common ratio = -3. Find the 7th term. a, = a(r)-1 O…

A: It is in gp

Q: Given the geometric progression Find the sum of the first 9 terms of the sequence. 7, 35, ...) 25 5…

A: Given GP is 725, 75, 7, 35, ...

Q: The third term of a geometric sequence is 5, and the sixth term is -40. Find the eighth term.

A: The nth term of a geometric sequence is given by an=a1rn-1, where a1 is the first term of the…

Q: (a) The first 3 terms of an arithmetic progression are ?, 5?, 7? − 4. Find (i) the value of ?,…

A:

Q: Which of the following is the correct first four terms of the geometric progression with initial…

A: Introduction: Geometric Progression (GP) is a type of sequence in mathematics in which each…

Q: *1. Given that x-3, 2x + 1 and 7x - 2 are the first three consecutive terms of an arithmetic…

A: As per bartleby guidelines, for more than one question only 1st one is to be answered. Please upload…

Q: is 28 and the 7th term is 448, then find the 9th term of this GP. Show all steps.

A: Introduction: A geometric progression is a sort of progression in which each term has a fixed ratio…

Q: In an arithmetic progression of n terms (n is even), the two middle terms are p-q.p+q respectively.…

A: The formula for the sum of squares of an arithmetic progression is: sum=2n-1d26+ad(n-1)+a2×n where,…

Q: Write an equation for the nth term of the given arithmetic

A:

Q: The 15th term of an arithmetic sequence is 21 and the common difference is -4. (a) Find the first…

A:

Q: The sum of three numbers in a geometric progression is 14. If the first two terms are each increased…

A:

Q: (c) The sum of the first 12 terms of a geometric sequence is 6144. If the common ratio is 2, find…

A:

Q: 2. The first three terms of either an arithmetic or geometric sequence are given by 6, a, 24. Which…

A: Given,         The first three terms of either an arithmetic or geometric sequence are…

Q: a) The third term of a geometric progression is -108 and sixth term is 32. Find: i) ii) The common…

A:

Q: The 4 term of a geometric progression is 2 and the seventh is 16 Find the geometric series 18 |

A:

Q: A machine is driving a 5.5 foot post into the ground. The first hit drives the post 18 inches into…

A: If machine run forever, post will driven into the ground by 48inch.

Q: The sixth term of a geometric sequence is 1215 and the third term is 45. Find the first term and the…

A:

Q: Which one of the following sequences is an arithmetic progression? O 3,6,12,24,48,. O 1,4,9,16,25. O…

A:

Q: Consider the sequence 8, 5, 2,-1.........-52 a) is the sequence an arithmetic progression? Why or…

A: Arithmetic Progression: A sequence is said to be an arithmetic progression, if the difference…

Q: For the arithmetic progression: 5+9+13+……   . Find the sum of the first 40 terms.

A: For the arithmetic progression: 5+9+13+…… n = 40 we have to find the sum of the first 40 terms, S40…

Q: The first term of a geometric sequence is 12, and the third term is 16/3. Find the fifth term.…

A: Given that first term of the geometric sequence is 12. Third term of the third term is 16/3. We have…

Q: A geometric progression has fårst term 16 and sum to infinity 40. The common ratio of the…

A: Sum of infinite geometric series, Sn=a/(1-r) Here, a is first term and r is common ratio. Given…

Q: {an} is an arithmetic progression with an non-zero common difference.the sum of all terms between…

A: Finding nth term of A. P progression whose value is 7

Q: An arithmetic progression has the first term of 32, the 5th term of 22 and the last term of −28.…

A:

Q: Three numbers are in an arithmetic progression with a common difference of 6. If 4 is subtracted…

A: Given data is : Common difference is 6 Let the three number in AP is a,a+6,a+12 From question , a-4…

Q: Write down the first five terms of the geometric sequence which has first term 1 and common ratio ½.

A: First term = a = 1 Common ratio = r = 1/2

Q: 2. Find the first three terms of geometric Progression whose sum is 342 and product is 74,088 Let…

A: Solution : First three terms of GP are, ar,a,ar Sum of first three terms of GP=342 ar+a+ar=342  …(1)…

Q: How would you determine whether a sequence is Arithmetic? How would you determine whether a…

A:

Q: The fifth term of an arithmetic sequence is 24, and the sum of the first 10 terms is 265. Write the…

A:

Q: In an arithmetic sequence the ratio of the third to the eight term is 6:1 and the sum of the third…

A:

Q: Given a geometric sequence whose first term is 3 and its common ratio is Find i) the 8 term, ii) the…

A: a=3  &  r=12. i. Eighth term is, T8=ar7    ∵Tn=arn-1=3127=3128

Q: An arithmetic progression has first term 11 and fourth term 32. The sum of the first nine terms is?

A: Formula,   S(n) = (n/2) * [2a + (n-1)*d]

Q: Which one of the following sequences is a geometric progression? 3,6,12,24,48,. O 1,4,9,16,25,. O…

A:

Q: Which term in this sequence would first exceed or equal 32,000?  What is the sum from the 1st term…

A: Given GP - 3100, 4247 ......4247 is the term which will exceed the 3200.Hence, only one term 4247…

Q: Find the sum of the first 15 terms of the geometric sequence shown below. 2, 6, 18, 54. . The sum of…

A: Given geometric sequence is: 2, 6, 18, 54, ...

Q: 3. The sum of three numbers in geometric progression is 52. If 8 is added to the middle number, the…

A: “Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: The fourth term of an arithmetic sequence is 11, and the sixth term is 17. Find the second term.

A:

Q: A machine is driving a 4.5 foot post into the ground. The first hit drives the post 16 inches into…

A: Solution is as below

Q: Given the sequence of numbers: {-3,9,-27,..} a) What kind of set is the sequence? b) What kind of…

A:

Q: The first three terms of an arithmetic progression are h - 2, 5k - 1, 2h + k, ... Express k in terms…

A: Given that the first three terms of an arithmetic progression are h - 2, 5k - 1, 2h + k, ... . we…

Q: The tenth term of an arithmetic sequence is 32, and the fifth term is 16. Find a, d, and the 20th…

A: Given: The tenth term of the arithmetic sequence is 32. The fifth term of the arithmetic sequence is…

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.