Question

if the sum of first 7terms of an Ap is49 and that of 17terms is289 ,find the sum of first n terms

Answer 1

s7=7/2[2a+(7-1)d]
49=7/2[2a+6d]
98=14a+42a
dividing both sides by 14
7=a+3d
a=7-3d________•1
now,
s17=17/2 [2a+(17-1)d]
289=17/2(2a+16d)
578 =34a+272d
dividing both sides by 34
17=a+8d
putting value of a from eq 1
17=7-3d+8d
10=5d
d=2
so,a=1
therefore sum of n terms =n/2 [2+(n-1)2]
=>n/2 (2+2n-2)
=>n/2 (2n)
=>n^2