Precalculus with Limits: A Graphing Approach
Precalculus with Limits: A Graphing Approach
7th Edition
ISBN: 9781305071711
Author: Ron Larson
Publisher: Brooks/Cole
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Chapter 8.3, Problem 40E
To determine

To find: an expression for nth term and the 7h term of the geometric sequence.

Expert Solution & Answer
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Answer to Problem 40E

An expression for nth term is an=3(12)n1 .

The 7thterm of the geometric sequence will be a7=128994509 .

Explanation of Solution

Given information:

Three terms of the sequence are given by,

  3,36,432,...

Concept used:

The general term of geometric sequence is given by formula

  an=a1rn1

Here, a1 is the first term and r is common ratio.

Every geometric sequence can be written in the following form.

  a1=a1,a2=a1r,a3=a1r2,a4=a1r3,...,an=a1rn1,..

Calculation:

Consider the given sequence.

  3,36,432,...

Now a2=a1r21

  36=3rr=363r=12...............(1)

Now, obtain the expression for nth term as shown:

  an=a1rn1=3×(12)n1

Thus, an expression for nth term is an=3(12)n1 .

Now, calculate the value of a7 by using the formula as shown:

  a7=a1r71a7=a1r6a7=3×(12)6a7=128994509

Hence, the 7thterm will be a7=128994509 .

Chapter 8 Solutions

Precalculus with Limits: A Graphing Approach

Ch. 8.1 - Prob. 11ECh. 8.1 - Prob. 12ECh. 8.1 - Prob. 13ECh. 8.1 - Prob. 14ECh. 8.1 - Prob. 15ECh. 8.1 - Prob. 16ECh. 8.1 - Prob. 17ECh. 8.1 - Prob. 18ECh. 8.1 - Prob. 19ECh. 8.1 - Prob. 20ECh. 8.1 - Prob. 21ECh. 8.1 - Prob. 22ECh. 8.1 - Prob. 23ECh. 8.1 - Prob. 24ECh. 8.1 - Prob. 25ECh. 8.1 - Prob. 26ECh. 8.1 - Prob. 27ECh. 8.1 - Prob. 28ECh. 8.1 - Prob. 29ECh. 8.1 - Prob. 30ECh. 8.1 - Prob. 31ECh. 8.1 - Prob. 32ECh. 8.1 - Prob. 33ECh. 8.1 - Prob. 34ECh. 8.1 - Prob. 35ECh. 8.1 - Prob. 36ECh. 8.1 - Prob. 37ECh. 8.1 - Prob. 38ECh. 8.1 - Prob. 39ECh. 8.1 - Prob. 40ECh. 8.1 - Prob. 41ECh. 8.1 - Prob. 42ECh. 8.1 - Prob. 43ECh. 8.1 - Prob. 44ECh. 8.1 - Prob. 45ECh. 8.1 - Prob. 46ECh. 8.1 - Prob. 47ECh. 8.1 - Prob. 48ECh. 8.1 - Prob. 49ECh. 8.1 - Prob. 50ECh. 8.1 - Prob. 51ECh. 8.1 - Prob. 52ECh. 8.1 - Prob. 53ECh. 8.1 - Prob. 54ECh. 8.1 - Prob. 55ECh. 8.1 - Prob. 56ECh. 8.1 - Prob. 57ECh. 8.1 - Prob. 58ECh. 8.1 - Prob. 59ECh. 8.1 - Prob. 60ECh. 8.1 - Prob. 61ECh. 8.1 - Prob. 62ECh. 8.1 - Prob. 63ECh. 8.1 - 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Sequences and Series Introduction; Author: Mario's Math Tutoring;https://www.youtube.com/watch?v=m5Yn4BdpOV0;License: Standard YouTube License, CC-BY
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