Answer :

Given: S_{7} = 49, S_{17} = 289

Sum of n terms of an A.P is given by the formula,

S_{7} = 49

Therefore,

⇒ 49 = 7(a + 3 d)

⇒ 7= a + 3 d

⇒ a + 3 d = 7 [1]

Similarly,

289 = 17(a + 8 d)

17 = a + 8 d

a + 8 d = 17 [2]

Subtracting [1] from [2] we get;

a + 8 d – a – 3 d = 17 – 7

⇒ 5 d = 10

⇒ d = 2

Using the value of d in the equation [1], we can find 'a' as follows:

a + 3 d =7

⇒ a + 6 = 7

⇒ a = 1

Using the values of a and d; we can find the sum of first n terms as follows:

⇒ S = n^{2}

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