Question

in an AP the 8th term is equal to the sum of the first 8 terms . show that the 4th term must be 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 = S8

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

hence proved

Answer 2

Step-by-step explanation:

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