If the sum of first 7 terms of an AP is 49 and that of 17 terms is 289, find the sum of first n terms.

Explanation

given that `s_7 = 49 = 7^2 (s_n = n^2)`

`s_17= 289 = 17^2 `

now `s_n=n/2[2a+ (n-1)d]`

`s_7= 7/2[2a+(7-1)d]`

`49= 7/2[2a+6d]`

`7=a+3d` eqn(1)

now `S_17= 17/2[2a+(17-1)d]`

`289= 17/2[2a+ 16d]`

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