Question

the sum of the third and seven terms of an A.P is 6 and this product is 8 find sn

Answer 1

let the 3rd Term be A + 2D
let the 7th term be A + 6D
》 3rd term + 7th term = 6
》2A + 8D = 6
》 A + 4D = 3

》 (A + 2D)(A + 6D) = 8
》 (A + 4D - 2D)(A + 4D + 2D) = 8
》 (3 - 2D)(3 + 2D) = 8
》 9 - 4D = 8
》 4D = 1
》 D = 0.25
》 A + 4D = 3
》 A + 4×0.25 = 3
》 A = 2

Sn = (n/2)(2A + (n-1) d)
Sn = (n/2)(4 + n/4 - 1/4)
Sn = (n/2)(n/4 + 15/4)
Sn = (n/2)((n+15)/4)
Sn = (n×(n+15)/8)