Exercise 6. Find the sum of the first eight terms in the geometric sequence: 100, 100(1.08), 100(1.08²), ….

Q: The 12th term of an arithmetic sequence is 59, and the fifth term is 31, Find the 20th term. 820 =

A: Topic = Sequence

Q: Find the sum to infinity of the geometric sequence given below 5. 16, 4, 1, ... 6. aj= 1000, r =…

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Q: Find the sum to infinity of the geometric sequence. 1/3, 1/9, 1/27, 1/81, …

A: Given series is 13,19,127,181From here a1=13 and a2=19We know that r=a2a1=1913=13

Q: Find the sum of the first 14 terms of the geometric sequence: -1/24, 1/12, -1/6, 1/3 , . . . .

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Q: た 2 白 Find the sum of the indicated number of terms of the geometric sequence. -4, 12, -36, ...; n =…

A: Consider the given series.

Q: Find the infinite sum of the geometric sequence with a = 2, r = 3 if it exists. -

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Q: Determine the sum of the geometric sequence if it exist. If the sum does not exist, write DNE. 8,…

A: Given,            A sequence is 8,-12,18,27,.....We know that,           A sequence is in Geometric…

Q: Find the 2nd, 3rd, and 4th terms of the geometric sequence whose first term is 6 and common ratio is…

A: The nth term of a sequence can be obtained by the formula an=arn-1,where r is the common ratio and…

Q: Find the explicit formula for the Arithmetic sequence. -5, 2,9, 16, ...

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Q: Write an expression that gives the requested term. The 12th term of the geometric sequence with the…

A: First term of geometric series  is given as;  a1=10   and   common ratio  is  r=3  aim to find the…

Q: 2a. Find a formula for the nth term of the arithmetic sequence below. 1,_,4, , 7, ...

A: Solve by formula

Q: 9. What is the sum of the first 15 terms of the arithmetic sequence -8, 7, 22, 37, . * O 202 O 1455…

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Q: 1. What are the two rules that represent a geometric sequence? Write each rule below and describe…

A: Rules for Geometric sequence is as below : [a]   xn=arn-1where, a= first termr=common rationso…

Q: Find the 10th element of the following arithmetic sequence, counting 7 as the first. 7,11,15,19,...

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Q: Write the first five terms of the geometric sequence whose first term is 6, and whose common ratio…

A: The answer is found in step-2

Q: To find the 40th term of the geometric sequence 8, 6, , which formula is correct? 39 8(4) a40 39 O…

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Q: What is the explicit formula for a geometric sequence?

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Q: 2.) Write the general formula for un for the arithmetic sequence 12, 4, –4, –12, ...

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Q: What is a common ratio of the geometric sequence whose first term is 5 and third term is 245? 5 1)7…

A: The geometric series has first term is 5 and the third term is 245   Geometric sequence formula:…

Q: Find the 10" term of the following geometric sequence. 4, 20, 100, 500,

A: A sequence is a function with domain being the set of natural numbers and the range being the set of…

Q: Find the nth partial sum of the arithmetic sequence for the given value of n. 0,-9, -18, -27, ... n…

A: As we know that; The formula for the nth partial sum of arithmetic sequence is: Sn=na1+an2 Where; a1…

Q: 15. Find the 5th term of the geometric sequence whose common ration is and whose first term is 7.

A: Given first term is 7 and common ration is 1/2 Here a=7,r=1/2

Q: Find the sum to infinity of the geometric sequence given below 1. 12, 4. .. .... 2. 900, 9, 0.09,...…

A: 1): Hera1=12a2=4a3=34This is not a geometric progression as a1a2 and a2a3 are not equal.SO, it is…

Q: Find the sum of the first 12 terms of the geometric sequence shown below. 3 2 . 3,-6, 12, The sum of…

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Q: Write the first six terms of the geometric sequence with the first term, a1, and common ratio, r. a1…

A: We have to solve given problem:

Q: Find the sum of the first 12 terms of the geometric sequence shown below. 4​,12,,36,108,...   the…

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Q: Find the common ratio of the geometric sequence: {2, – 10, 50, – 250, 1250, ...} -

A: Topic - sequence and series r = common ratio r = an+1/an

Q: find the first five terms of the geometric sequence.

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Q: Complete the explicit formula for the arithmetic sequence 5,14,23,32,41,50,.. An

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Q: Find the nth term of the arithmetic sequence {a,} whose initial term a and common difference d are…

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Q: Find the 14 term of the following geometric sequence. 4, 8, 16, 32, ... O

A: The geometric sequence is given as: 4, 8, 16, 32, …. We need to calculate the 14th term of the…

Q: Find the sum of the first 14 terms of the geometric sequence shown below. 2, 6, 18, 54,... ***** The…

A: Given, Geometric sequence 2, 6, 18, 54 .... The objective is to find the sum of the first 14 terms.…

Q: 6. Write an explicit formula for the geometric sequence 33, 99, 297, 891, ..

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Q: Find the sum of the first 14 terms of the geometric sequence shown below. 2, 6, 18, 54, .. The sum…

A: Given that :  2 , 6,18,54,..... By using geometric sequence...  r = difference ratio.  a = first…

Q: Write a recursive formula for the geometric sequence an given below. 10,10/3,10/9,10/27,10/81,…

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Q: Determine the sum of the geometric sequence if it exist. If the sum does not exist, write DNE. 2, ½,…

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Q: Find the nth term of the geometric sequence whose initial term is a1=1a1=1 and common ratio is 77.

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Q: Find the infinite sum of the geometric sequence with 3 if it exists. a = 2, r =

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Q: Find the explicit formula for the general nth term of the arithmetic sequence described below.…

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Q: What is the common ratio of the geometric sequence whose first term is 27 and fourth term is 64? 1)…

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Q: Find the common ratio of the geometric sequence 40, 30, 22-

A: Given series is, 40,30,2212,...

Q: What is the common ratio of the geometric sequence 10, 20, 40, 80, 160?

A: Common ratio is the constant factor between consecutive terms of a geometric sequence. To find…

Q: Write an explicit formula for the geometric sequence  4.  – 4/3, 4/9, -4/27, …

A: Calculation are as follows

Q: 1. When is a list of numbers called a geometric sequence ? 2. In what ways can you express a…

A: This problems are related to sequence and series.

Q: i i=0

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Q: Write the first four terms of the geometric sequence satisfying the following conditions: a, = 2,…

A: In general, The geometric sequence is, a, ar, ar2, ar3,.....    where, a= first term, r=common ratio…

Q: find the explicit formula for the general nth term of the geometric sequence…

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Q: 3. -5, 15, -45,... n = 7

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Q: For Exercise, find the number of terms of the finite arithmetic sequence  11, 10.7, 10.4, 10.1, … ,…

A: Given, terms of the finite arithmetic sequence11, 10.7, 10.4, 10.1, …  −3.4

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.