Precalculus with Limits: A Graphing Approach

7th Edition

ISBN: 9781305071711

Author: Ron Larson

Publisher: Brooks/Cole

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Concept explainers

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.

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Question

Chapter 8, Problem 53RE

To determine

To determine the first five terms of the Geometric sequence-

$a1=120,ak+1=13ak$

Expert Solution & Answer

Answer to Problem 53RE

Thefirst five terms of the Geometric Sequence are $120,40,403,409,4027$ .

The Common ratio is $13$ .

The $nth$ term is $120(13)n−1$ .

Explanation of Solution

Given:

Sequence - $a1=120,ak+1=13ak$

Formula Used:

$nth$ term of the Geometric sequence is given as $tn=arn−1$

Calculation:

Given sequence: $a1=120,ak+1=13ak$

$a2=13(120)a2=40$

$a3=13(40)a3=403$

$a4=13(403)a4=409$

$a5=13(409)a5=4027$

The first five terms of the Geometric Sequence are $120,40,403,409,4027$ .

Common ratio $=$ $r=a2a1$

$r=40120r=13$

The common ratio is $13$ .

$nth$ term is $tn=arn−1$

$tn=120(13)n−1$

The $nth$ term is $120(13)n−1$ .

Conclusion:

Hence, the first five terms of the Geometric Sequence are $120,40,403,409,4027$ .

The Common ratio is $13$ .

The $nth$ term is $120(13)n−1$ .

Chapter 8, Problem 52RE

Chapter 8, Problem 54RE

Chapter 8 Solutions

Precalculus with Limits: A Graphing Approach

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Prob. 93RE Ch. 8 - Prob. 94RE Ch. 8 - Prob. 95RE Ch. 8 - Prob. 96RE Ch. 8 - Prob. 97RE Ch. 8 - Prob. 98RE Ch. 8 - Prob. 99RE Ch. 8 - Prob. 1CT Ch. 8 - Prob. 2CT Ch. 8 - Prob. 3CT Ch. 8 - Prob. 4CT Ch. 8 - Prob. 5CT Ch. 8 - Prob. 6CT Ch. 8 - Prob. 7CT Ch. 8 - Prob. 8CT Ch. 8 - Prob. 9CT Ch. 8 - Prob. 10CT Ch. 8 - Prob. 11CT Ch. 8 - Prob. 12CT Ch. 8 - Prob. 13CT Ch. 8 - Prob. 14CT Ch. 8 - Prob. 15CT Ch. 8 - Prob. 16CT Ch. 8 - Prob. 17CT Ch. 8 - Prob. 18CT Ch. 8 - Prob. 19CT Ch. 8 - Prob. 20CT Ch. 8 - Prob. 21CT Ch. 8 - Prob. 22CT Ch. 8 - Prob. 23CT Ch. 8 - Prob. 24CT Ch. 8 - Prob. 25CT Ch. 8 - Prob. 26CT

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the first five terms of the Geometric sequence- a 1 = 120 , a k + 1 = 1 3 a k

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