   Chapter 13.3, Problem 7E ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

#### Solutions

Chapter
Section ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742
Textbook Problem

# SKILLS 5 − 8 n t h Term of a Geometric Sequence The n t h term of a geometric sequence is given. (a) Find the first five terms of the sequence. (b) What is the common ratio r ? (c) Graph the terms you found in (a). a n = 5 2 ( − 1 2 ) n − 1

To determine

(a)

To find:

The first five terms of the sequence for an=52(12)n1.

Explanation

Given:

The nth term of the sequence is an=52(12)n1.

Approach:

A geometric sequence is a sequence of the form:

a, ar, ar2,…

The number a is the first term, and r is the common ratio of the sequence.

The nth term of the a geometric sequence is given as,

an=arn1(1)

Calculation:

Suppose first term is a1, second term is a2, third term is a3, fourth term is a4, and fifth term is a5.

The nth term is given as,

an=52(12)n1(2)

Substitute 1 for n in equation (2), to calculate the first term:

a1=52(12)n1=52(12)0=52

Substitute 2 for n in equation (2), to calculate the second term:

a2=52(12)n1=52(12)1=52×12=54

Substitute 3 for n in equation (2), to calculate the third term:

To determine

(b)

To find:

The common ratio of the sequence.

To determine

(c)

To graph:

The terms of part (a).

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