An important and exam oriented question from arithmetic progression chapter as it was already asked in previous year paper of 2012 in which we have been asked to find the common difference of an AP whose first term is 5 and the sum of its first four terms is half the sum of the next four terms.

Book – RS Aggarwal, class 10, chapter 5A, question no 34

## Let d be the common difference of given A.P.

First term (a)=5

Given:-

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

⇒a+(a+d)+(a+2d)+(a+3d)=1/2[(a+4d)+(a+5d)+(a+6d)+(a+7d)]

⇒4a+6d=1/2(4a+22d)

⇒4a+6d=2a+11d

⇒11d−6d=4a−2a

⇒d=(2×5)/5=2

Hence the common difference of given A.P. is 2.