The 3rd term of an arithmetic sequence is - 1 and the 7th term is - 13. Find the explicit formula for this sequence. What is a22?

Hopefully the math terms won't confuse anyone.

So in the series, a_3 = - 1 and a_7 = - 13. Since it's an arithmetic sequence, all the terms in the series can be represented as:

a_n = a_0 + n * k

where n is the nth number. K is a constant you add to reach the next term, and a_0 is the starting constant.

a_7 = a_0 + 7 * k

a_3 = a_0 + 3 * k

solving this system gives you that

k = - 3 and a_0 = 8

Hence:

a_22 = 8 + 22 * - 3 = - 58