# 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.

Given: S7 = 49, S17 = 289
Sum of n terms of an A.P is given by the formula,

where, S = Sum, n = number of terms, a = first term and d = common difference.

S7 = 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 = n2

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