arithmetic
posted by swathi .
find the common difference of A.P whose first term is 5 and the sum of its first 4 terms is half the sum of next 4 terms

Let the common difference be d.
The sum of the first four terms is
5 + (5+d) + (5+d+d) + (5+d+d+d)
= 20 + 6d
The sum of the next 4 terms is
5+4d + 5+5d + 5+6d + 5+7d = 20 + 22d
You have been told that
20 +6d = (1/2)(20 + 22d)= 10 + 11d
Therefore
5d = 10
d = 2
Check: does
5+7+9+11 = (1/2)(13+15+17+19) ?
32 = (1/2)(64) 
ask your teacher