Question

In an AP, if the sum of first seven terms is 49 and that of seventeen terms is 289, find the sum of first n terms.

Answer 1

S7 = 49
S17 = 289

Sn = n/2(2a+(n-1)d)
S7 = 7/2(2a+(7-1)d)
=> 7/2(2a+7d-d) = 49
=> 7/2(2a+6d) = 49
=> 2a+6d = 14 -----------i

S17 = 17/2(2a+(17-1)d)
=> 17/2(2a+17d-d) = 289
=> 17/2(2a+16d) = 289
=> 2a+16d = 34 -------------ii

Using Elimination method

2a+6d = 14
2a+16d = 34
---------------------
-10d = -20
-d = -2
d = 2
--------------------

2a+6d = 14
=> 2a +6x2 = 14
=> 2a +12 = 14
=> a = 1

Sn = n/2(2x1+(n-1)2)
= n/2 (2+2n-2)
= n/2x2(1+n-1)
= nxn
n²



HOPE IT HELPS YOU !!!!!