Question

find common difference of an arithmetic progression whose first term is 5 and the sum of the first 4 terms is the half of the sum of next 4 terms

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

a = 5

Since, sum of first four terms is half the sum of next four terms

i.e. a1 + a2+a3 + a4 = 1/2(a5+a6+a7+a8)

a1 + a2+a3 + a4 = 1/2[(a1 + a2+a3 + a4+a5+a6+a7+a8) - (a1 + a2+a3 + a4)] (Adding and subtracting the sum of first four terms from the RHS)

i.e. S4 = 1/2(S8 - S4)

i.e. 2 S4  = S8 - S4 

3S4  = S8