Question

find the common diffrence of an ap whose first term is 5 and the sum of its first 4 term is half the sum of the next four term

Answer 1

a=5
s4=1/2(s8-s4)

: s4=2{2a+3d} ...............(1)
: s8=4{2a+7d}
: s8-s4=8a+28d-4a-6d
: s8-s4=4a+22d
: s4=1/2(s8-s4)
: s4=1/2{4a+22d}
: s4=2a+11d ...................(2)
from 1 and 2
4a+6d=2a+11d

: 2a=5d
: 10=5d
: d=2