Question

If sum of first four terms of ap is 28 and next four terms is 100 find the ap

Answer 1

given S4=28 and S8 - S4=100
We know Sn=n/2(2a+(n-1)d
28=4/2(2a+(4-1)d
28=2(2a+3d)
14=2a+3d---------(1)
S8 - S4=100
S8 -28=100
S8=100-28
8/2(2a+(8-1)d)=72
4(2a+7d)=72
2a+7d=72/4
2a+7d=18-----------(2)
from (1) and (2)
2a+3d=14
2a+7d=18
-. -. -
---------------------
4d=4
d=1
put in (1)
2a+3(1)=14
2a=14-3
a=11/2
a2=a+d
=11/2+1
= 13/2
therefore the AP is 11/2,13/2.............