If the sum of 7 terms of an A.P. is 49 and that of 17 term is 289, find the sum of n terms.
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sum of seven terms S7=49
7/2(2a+6d)=49
2a+6d=14
a+3d=7
S17=289
17/2(2a+16d)=289
2a+16d=34
a+8d=17
solving above equations using elimination method
5d=10
d=2
put d=2 in 1
a+3d=7
a+6=7
a=1
Sn=n/2(2a+(n-1)d)
=n/2(2×1+(n-1)2)
=n/2(2+2n-2)
=n/2(2n)
=n²
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