Q. 344.4( 13 Votes )

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.

Answer :

Let a be the first term and d be the common difference of the AP.

Given: a = 5


Sum of first four terms = 1/2(sum of next four terms)


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


2a = 5d


d = 2a/5


As a = 5, therefore,


d = 10/5 = 2


Thus, Common difference = d = 2


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