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Chapter 12: Q 100. (page 1184)

Find the fifteenth term of a sequence where the tenth term is −11 and the common difference is −3. Give the formula for the general term.

Short Answer

Expert verified

The fifteenth term is -26 and the general term is an=−3n+19.

Step by step solution

01

Step 1. Given Information.

The tenth term is −11 and the common difference is −3.

02

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

Substitute 10 for n, -3 for d, and the tenth term is -11, in the formula an=a1+n−1k.

a10=a1+10−1−3−11=a1−27a1=16

03

Step 3. Find the fifteenth term.

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

a15=16+15−1−3=16−42=-26

04

Step 4. Find the general terms.

To find the general terms, substitute the first term 16 and the common difference -3 in the formula.

an=16+n−1−3=16−3n+3=−3n+19

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