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

Given,

a₄ + a₈ = 24;

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

2a + 10d = 24 ⇒ a+5d = 12 → 1

We have been also given that

a₆ + a₁₀ = 44

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

2a + 14d = 44 ⇒ a +7d = 22 → 2

By subtracting two equations

(a + 5d) - (a + 7d) = 12 – 22

-2d = -10

d = 5

Substitute d in any one of the equation.

a+5d = 12

a + 5×5 = 12

a = 2

The first 3 terms of the series is given by a, a+d, a+2d

⇒ 2, 2+5, 2+2×5

⇒ 2, 7, 12