Question

if the sum of 7 terms of an ap is 49 and that of 17 terms is 289 find the sum of first n terms

Answer 1

S7=7/2 (2a+(7-1)d)
49 =7/2 (2a+6d)
49×2=7 (2a+6d)
98=14a+42d
dividing both sides by 14
7=a+3d
a=7-3d____________○1

again, ATQ
S17=17/2 (2a+(17-1)d)
289=17/2 (2a+16d)
289×2=17 (2a+16d)
578=34a+272d
dividing both sides by 34.
17=a+8d ______________○2
putting value of a from ○1 in ○2
17=7-3d+8d
17=7-5d
17-7=5d
10=5d
d=10/5
d=2
putting value of d in eq○1
a=7-(3×2)
a=7-6 =>a=1
now,
Sn=n/2 (2a+(n-1)d
=>n/2 (2+(n-1)2)
=>n/2 (2+2n-2)
=>n/2(2n)
=>n^2
hope it helps u....!!!