In a particular arithmetic progression, the sum of the first 10 terms is equal to the sum of the first twenty terms. Show that the sum of the first 30 terms is equal to 0.

Answer 1

10/2 (2a+9d) = 20/2 (2a+19d)
20a+90d = 40a+380d
20a+290d = 0
2a+29d = 0

S30 = 30/2 (2a+29d) = 0