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Chapter 12: Q 155. (page 1198)

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

Find a10of the sequence,1,0.1,0.01,0.001,0.0001,0.00001,...

Short Answer

Expert verified

The value of a10is0.000000001and the general term for the sequence is an=(0.1)n-1.

Step by step solution

01

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

The given sequence is:

1,0.1,0.01,0.001,0.0001,0.00001,...

First term:

a1=1

Common ratio:

0.11=0.1,0.010.1=0.1,0.0010.01=0.1,0.00010.001=0.1,0.000010.0001=0.1r=0.1

02

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

an=a1rn-1

Substitute a1=1,r=0.1and n=10in the formula,

role="math" localid="1645356029281" a10=(1)(0.1)10-1=(1)(0.1)9=0.000000001

a10=0.000000001

03

Step 3.  Find the general term.

Substitute a1=1and r=0.1in the formula,

localid="1645356302093" an=a1rn-1an=1(0.1)n-1an=(0.1)n-1

The general term for the sequence is an=(0.1)n-1.

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