Question

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

Answer 1

Given

t₄ + t₈ = 24

`=>` (a + 3d) + (a + 7d) = 24

`=>` 2a + 10d = 24

`=>` a + 5d = 12  ...(i) 

And,

t₆ + t₁₀ = 44

`=>` (a + 5d) + (a + 9d) = 44

`=>` 2a + 14d = 44

`=>` a + 7d = 22   ...(ii)

Subtracting (i) from (ii), we get

2d = 10

`=>` d = 5

Substituting value of d in (i), we get

a + 5 × 5 = 12

`=>` a + 25 = 12

`=>` a = -13 = 1^st term

a + d = -13 + 5 = -8 = 2^nd term

a + 2d = -13 + 2 × 5 = -13 + 10 = -3 = 3^rd term

Hence, the first three terms of an A.P are -13, -8 and -3