Question

If the sum of first 7 terms of an arithmetic sequence is 49 and the sum of next 10 terms is 240 find the sum of first n terms

Answer 1

s7=49
7/2[2a+(7-1)d=49
2a+6d=49×2/7
2a+6d=14
a=14-6d/2 (equation 1)
s10=240
10/2[2a+(10-1)d=240
5[2a+9d=240
2a+9d=48
Putting the value of a
2(14-6d/2)+9d=48
2(7-3d)+9d=48
6d=34
d=34/6 =17/3
Putting the value of d in eq 1
a=7-3d
=7-3(17/3)
=7-17
=-10
Sn=n/2[2a+(n-1)d
=n/2[2×-10+(n-1)17/3
=n/2[-20+17/3n-3]
=n/2[-23+17/3]