the sum of 4th and 8th terms of an AP is 24 and the sum of 6th and 10th terms is 44. find the first 3 terms of the AP.

Let the first term of an A.P.=a

and the common difference of the given A.P.=d

As we know that,

a _n = a + (n − 1) d

a ₄ = a + (4 − 1) d

a ₄ = a + 3d

Similarly,

a ₈ = a + 7d

a ₆ = a + 5d

a ₁₀ = a + 9d

Sum of 4^th and 8^th term =  24  (Given)

a ₄ + a ₈ = 24

a + 3d + a + 7d = 24

2a + 10d = 24

a + 5d = 12.................... (i)

Sum of 6^th and 10^th term = 44  (Given)

a ₆ + a ₁₀ = 44

a + 5d + a + 9d = 44

2a + 14d = 44

a + 7d = 22 ......................(ii)

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

From equation (i), we get,

a + 5d = 12

a + 5 (5) = 12

a + 25 = 12

a = −13

a ₂ = a + d = − 13 + 5 = −8

a ₃ = a ₂ + d = − 8 + 5 = −3

∴The first three terms of this A.P. are −13, −8, and −3.