Question

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

Answer 1

Given: a₄ + a₈ = 24

⇒ a +3d + a + 7d = 24

⇒ 2a + 10d = 24 …(i)

and a₆ + a₁₀ = 44

⇒ a +5d + a + 9d = 44

⇒ 2a + 14d = 44 …(ii)

Solving Linear equations (i) and (ii), we get

2a + 10d – 2a – 14d = 24 – 44

⇒ –4d = – 20

⇒ d = 5

Putting the value of d in eq. (i), we get

2a + 10×5 = 24

⇒ 2a + 50 = 24

⇒ 2a =24 –50

⇒ 2a =–26

⇒ a = –13

So, the first three terms are –13, –8, –3.