Question

the sum of first 7 terms of an AP is 49 and that of first 17 terms of it is 289 .find the sum of first n terms

Answer 1

S₇ = 49
S₁₇ = 289
we know that Sn = n/2 (2a+(n-1)d)
S₇ = 7/2 (2a+(7-1)d) =49   →(1)
S₁₇ = 17/2 (2a+(17-1)d) = 289  →(2)
on simplifying 
49 = 7/2 (2a+6d) ⇒ 2a+6d = 14 →(3)
289= 17/2 (2a+16d) ⇒ 2a+16d = 34  →(4)
on solving (3) &(4) we get,
d = 2

substituting d in (3)
2a+6*2 = 14
2a = 2
a=1
Sum of n terms (Sn) = n/2(2*1+(n-1)2)
 = n/2 (2+(n-1)2)
= n/2 (2+2n-2)
= n/2(2n)
= n²





Hope it helps.... :)