Question

What is the 24th term of the arithmetic sequence where a1 = 8 and a9 = 56?

Answer 1

`a_(24)=146`

Explanation:

The formula of a nth term of n arithmetic sequence:

`a_n=a_1+(n-1)d`

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`a_m=a_1+(m-1)d\\\\a_m-a_n=(a_1+(m-1)d)-(a_1+(n-1)d)\\\\=a_1+(m-1)d-a_1-(n-1)d=(m-1)d-(n-1)d=(m-1-n+1)d=(m-n)d`

Therefore

`a_9-a_1=(9-1)d=8d`

`8d=56-8\\8d=48\qquad|:8\\d=6`

Substitute:

`a_1=8,\ d=6,\ n=24\\\\a_(24)=8+(24-1)(6)=8+(23)(6)=8+138=146`