PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)

8th Edition

ISBN: 9781337904285

Author: Larson

Publisher: CENGAGE L

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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 8.3, Problem 41E

To determine

To find: an expression for nth term and the 10^h term of the geometric sequence.

Expert Solution & Answer

Answer to Problem 41E

An expression for nth term is $an=5(6)n−1$ .

The 10^t^hterm of the geometric sequence will be $a10=50388480$ .

Explanation of Solution

Given information:

Three terms of the sequence are given by,

$5,30,180,...$

Concept used:

The general term of geometric sequence is given by formula

$an=a1rn−1$

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

Every geometric sequence can be written in the following form.

$a1=a1,a2=a1r,a3=a1r2,a4=a1r3,...,an=a1rn−1,..$

Calculation:

Consider the given sequence.

$5,30,180,...$

Now $a2=a1r2−1$

$30=5rr=305r=6...............(1)$

Now, obtain the expression for nth term as shown:

$an=a1rn−1=5×(6)n−1$

Thus, an expression for nth term is $an=5(6)n−1$ .

Now, calculate the value of $a10$ by using the formula as shown:

$a10=a1r10−1a10=a1r9a10=5×(6)9a10=50388480$

Hence, the 10^t^hterm will be $a10=50388480$ .

Chapter 8.3, Problem 40E

Chapter 8.3, Problem 42E

Chapter 8 Solutions

PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)

Ch. 8.1 - Prob. 1E Ch. 8.1 - Prob. 2E Ch. 8.1 - Prob. 3E Ch. 8.1 - Prob. 4E Ch. 8.1 - Prob. 5E Ch. 8.1 - Prob. 6E Ch. 8.1 - Prob. 7E Ch. 8.1 - Prob. 8E Ch. 8.1 - Prob. 9E Ch. 8.1 - Prob. 10E

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an expression for nth term and the 10 h term of the geometric sequence.