Answer :

Given,

a_{4} + a_{8} = 24;

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

2a + 10d = 24 ⇒ a+5d = 12 → __1__

We have been also given that

a_{6} + a_{10} = 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

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