Question

 Find the common difference of an A.P. whose first term is 5 and the sum of first four terms is half the sum of next four terms.

Answer 1

Let a and d be the first term and common difference of A.P. respectively.
Given, a = 5
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)]`
⇒ 2(4a + 6d) = (4a + 22d)
⇒ 2(20 + 6d) = (20 + 22d)   ...(∵ a = 5)
⇒ 40 + 12d = 20 + 22d
⇒ 10d = 20
⇒ d = 2
Thus, the common difference of A.P. is 2.