Question

How many terms are in the arithmetic sequence 5, 1, −3, . . . , −111?

Answer 1

first term (a) = 5, common difference (d) = 1 - 5 = -4, last term (l) = -111

l = a + (n - 1)d
-111 = 5 + (n - 1) x -4 = 5 - 4n + 4 = 9 - 4n
4n = 9 + 111 = 120
n = 120/4 = 30

Therefore, there are 30 terms.