Question

The sum of 4^th and 8^th terms of an A.P. is 24 and the sum of the 6^th and 10^th terms is 44. Find the first three terms of the A.P.

Answer 1

Suppose a, a + d, a + 2d, a + 3d, ……., are in arithmetic progression, then according to the question,

∵ a₄ + a₈ = 24

⇒ (a + 3d) + (a + 7a) = 24

⇒ 2a + 10d = 24

⇒ a + 5d = 12        ...(1)

And a₆ + a₁₀ = 44

⇒ (a + 5a) + (a + 9d) = 44

⇒ 2a + 14d = 44

⇒ a + 7d = 22        ...(2)

⇒ 2d = 10             ...[From equation (2) – (1)]

⇒ d = `10/2`

⇒ d = 5

Putting the value of d in equation (1),

a + 5 × 5 = 12

⇒ a + 25 = 12

⇒ a = 12 – 25

⇒ a = –13

⇒ a₂ = a + d

⇒ a₂ = –13 + 5

⇒ a₂ = –8

And a = a + 2d

a = –13 + 5 × 2

a = –13 + 10

a = –3

Hence, the required first three terms of the given arithmetic progression are –13, –8 and –3 respectively.