# The sum of the first 7 terms of an AP is 49 and the sum of its first 17 terms is 289. Find the sum of its first n terms.

Let a be the first term and d be the common difference.

Given: S7 = 49, S17 = 289

To find: sum of first n terms.

Now, consider S7 = 49

(7/2)[2a + (7 - 1)d] = 49

(7/2)[2a + 6d] = 49

[a + 3d] = 7 …………(1)

Now, consider S17 = 289

(17/2)[2a + (17 - 1)d] = 289

(17/2) × [2a + 16d] = 289

[a + 8d] = 17 …………..(2)

Now, on subtracting equation (2) from equation (1), we get,

5d = 10

d = 2

from equation (1), we get

a = (7 - 3d)

a = 7 - 6

a = 1

a = 1, d = 2

Now, Sum of first n terms = Sn = (n/2)[2a + (n - 1)d]

= (n/2)[2 + (n - 1)2]

= (n/2)[2n]

= n2

Sn = n2

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