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