Question

find the common difference of an AP whose first term is 5 and the sum of its first four term is half the sum of the next four 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

Given first term(a) = 5
2 *sum of first four terms = sum of next four terms
2 * (5+5+d+5+2d+5+3d) = 5+4d+5+5d+5+6d+5+7d
2*(20+6d) = 20 + 22d
40 + 12d = 20 + 22d
40 - 20 = 10d
d = 20/10 = 2
Common difference = 2