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Chapter 12: Q 153. (page 1198)

In the following exercises, find the indicated term of the given sequence. Find the general term for the sequence.

Finda15of the sequence, -486,162,-54,18,-6,2,...

Short Answer

Expert verified

The value ofa15is -219,683 and the general term for the sequence isan=-486(-13)n-1.

Step by step solution

01

Step 1.  Write the given information, determine the first term and common ratio.

The given sequence is:

-486,162,-54,18,-6,2,...

First term is:

a1=-486

common ratio:

162-486=-13,-54162=-13,18-54=-13,-618=-13,2-6=-13

r=-13

02

Step 2. Use the formula of general term to find the twelfth term

an=a1rn-1

Substitute the values a1=-486,r=-13and n=15in the formula,

role="math" localid="1645354392163" a15=(-486)(-13)15-1=(-486)(-13)14=-219,683

a15=-219,683

03

Step 3.  Find the general term.

Substitute a1=-486and r=-13in the formula,

an=a1rn-1an=(-486)(-13)n-1

The general term of the sequence isan=-486(-13)n-1.

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