If the sum of first 7 terms of an A.P. is 49 and that of its first 17 terms is 289, find the sum of first n terms of the A.P.
Let the first term and the common difference of the given AP be a and d, respectively.
Sum of the first 7 terms, S7 = 49
⇒ a+3d=7 .....(1)
Sum of the first 17 terms, S17 = 289
⇒ a+8d=17 .....(2)
Subtracting (2) from (1), we get
⇒ d = 2
Substituting the value of d in (1), we get
a = 1
Sum of the first n terms is given by
Therefore, the sum of the first n terms of the AP is n2.