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
