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Chapter 12: Q. 270 (page 1218)

In the following exercises, find the indicated term and give the formula for the general term.

Find the twenty-first term of a sequence where the seventh term is 14and the common difference is -3.

Short Answer

Expert verified

The twenty-first term is -28.

The general term is an=35-3n.

Step by step solution

01

Step 1. Given Information

We are given that the seventh term is 14and the common difference is 鈭�3.

We have to find the twenty-first term of a sequence.

02

Step 2. Find the first term  

The seventh term is given by,

a7=14a1+(7-1)d=14a1+6d=14

Putting the value of common difference d=-3

role="math" localid="1645329689249" a1+6(-3)=14a1-18=14a1=14+18a1=32

03

Step 3. Find the twenty-first term

The twenty-first term is given by,

a21=a1+(21-1)da21=32+20(-3)a21=32-60a21==-28

Hence the twenty-first term is -28.

04

Step 4. Finding the general term

Now, putting the value of first term and common difference in an=a1+(n-1)d,

an=32+(n-1)(-3)an=32-3n+3an=35-3n

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