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.

Question

Philoid · Accepted 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