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Chapter 12: Q 151. (page 1198)

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

Find a9of the sequence,9,18,36,72,144,288,...

Short Answer

Expert verified

The value ofa9is2,304and the general term isan=9(2)n-1.

Step by step solution

01

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

The given sequence is:

9,18,36,72,144,288,...

First term is:

a1=9

Common ratio:

189=2,3618=2,7236=2,14472=2,288144=2

r=2

02

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

an=a1rn-1

Substitute the values a1=9,r=2and n=9in the formula

role="math" localid="1645347069708" a9=(9)(2)9-1=(9)(2)8=(9)(256)=2304

a9=2,304

03

Step 3. Find the general term.

Substitute a1=9and r=2into the formula,

an=a1rn-1an=(9)(2)n-1

The general term of the sequence isan=9(2)n-1.

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