Question

The sum of the first four terms is half of the sum of the next four terms and first term is 5 then find out the common difference

Answer 1

let d is common difference of AP
now first 4term is 5,5+d,5+2d,5+3d
and next 4term 5+4d,5+5d,5+6d,5+7d
now according to question 
20+6d=(20+22d)/2
20+6d=10+11d
d=2

Answer 2

S4=1/2(S8-S4)
a=5
so,4/2(2a+3d)=1/2{8/2(2a+7d) - 4/2(2a+3d)}
=>2(2×5+3d)=1/2{4(2×5+7d) - 2(2×5+3d)}
=>20+6d=1/2(40+28d - 20 - 6d)
=>20+6d=1/2(20+22d)
=>20+6d=10+11d
=>11d-6d=20-10
=>5d=10
=>d=10/5=2