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Chapter 11: Q 96. (page 1069)

Find the thirteenth term of a sequence where the sixth term is −1 and the common difference is −4. Give the formula for the general term.

Short Answer

Expert verified

The thirteenth term is -29 and the general term is an=−4n+23.

Step by step solution

01

Step 1. Given Information.

The sixth term is −1 and the common difference is −4.

02

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

Substitute 6 for n,-4 for d, and the sixth term is -1, in the formula an=a1+n−1d.

localid="1645353125301" a6=a1+6−1−4−1=a1−20a1=19

03

Step 3. Find the thirteenth term.

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

a13=19+13−1−4=19−48=-29

04

Step 4. Find the general terms. 

To find the general terms, substitute the first term 19 and the common difference -4 in the formula.

an=19+n−1−4=19−4n+4=−4n+23

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