Question

In an AP, the 8th term is equal to the sum of the first 8
terms. Show that the 4th term is 0

Answer 1

let the first term of an A.P. is 'a' and common difference 'd'

∴ 8th term = sum of the first 8 terms

a8 = S

a + 7d = 8/2(2a + (8 - 1)d)

a + 7d = 8/2(2a + 7d)

2a + 14d = 16a + 56d

16a + 56d - (2a + 14d) = 0

14a + 52d = 0

divide eq. by 14 we get ,

a + 3d = 0

and a + 3d = a4 = 0