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Chapter 12: Q 98 (page 1184)

Find the fifteenth term of a sequence where the tenth term is 17 and the common difference is seven. Give the formula for the general term.

Short Answer

Expert verified

The fifteenth term is 144 and the general term isan=7n+39.

Step by step solution

01

Step 1. Given Information.

The tenth term is 17 and the common difference is seven.

02

Step 2. Find the first term by using the arithmetic formula.

Substitute 10 for n, 7 for d, and the tenth term is 17, in the formula an=a1+n−1d.

a10=a1+10−1717=a1+63a1=63−17=46

03

Step 3. Find the fifteenth term.  

Use the first term and the common difference to find the fifteenth term.

a15=46+15−17=46+98=144
04

Step 4. Find the general terms.

To find the general terms, substitute the first term 46 and the common difference 7 in the formula.

an=46+n−17=46+7n−7=7n+39

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