Question

Given an arithmetic sequence with `d=-7` and `a_7=4`, what is `a_22`?

Answer 1

`a_22=-101`

Explanation:

`n^(th)` term of an arithmetic sequence, whose first term is `a_1` and common difference is `d` is `a_n=a_1+(n-1)d`.

As `a_7=a_1+(7-1)d=4`, we have

`a_1+6xx(-7)=4`

or `a_1=4+42=46`

and hence `a_22=46+(22-1)*(-7)`

`=46-21xx7`

`=46-147`

`=-101`