Q. 294.7( 16 Votes )

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.

Answer :

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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