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Chapter 12: Q. 21 (page 838)

In Problems 20 and 21, find a general formula for each arithmetic sequence.

10th term is 0

18th term is 8

Short Answer

Expert verified

The general formula of the sequence is:an=n-10

Step by step solution

01

Step 1. Given information 

In an arithmetic sequence :

a10=0a18=8

Let ais the first term and dis the common difference of the sequence.

02

Step 2. Make two equations of a and d

According to the given condition,

a10=0a+(10-1)d=0

.a+9d=0.......... equation (1)

a18=8a+(18-1)d=8.

a+17d=8...............equation (2)

03

Step 3. Solve equations. 

Substract equation (1) from (2)

(a+17d)-(a+9d)=8-08d=8d=1

Substitute this value in the equation (1)

a+9.1=0a+9=0a=-9

04

Step 4. General formula for sequence. 

Substitute values of aandd in general formula of arithmetic sequence.

an=a+(n-1)d=-9+(n-1).1=-9+n-1=n-10

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