Question

if the sum of first 7 terms of an ap is 49 and that of first 17 terms of 2 is 289 . find its first n terms

Answer 1

Sn=n/2(2a+{n-1}d)
49=7/2(2a+{7-1}d)
49×2=7(2a+6d)
98=14a+42d....(divide the whole equation by 14)
7=a+3d......(i)
289=17/2(2a+{17-1}d)
289×2=17(2a+16d)
578=34a+272d....(divide the whole equation by 34)
17=a+8d......(ii)
by subtract equation (i) from equation (ii)
a+8d-(a+3d)=17-7
a+8d-a-3d=10
5d=10
d=2
by putting the value of d in equation (i)
a+3d=7
a+3×2=7
a=7-6
a=1
1,6,11,........