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

Let the first term of the AP = a and common difference = d
According to first condition, a₄ + a₈ = 24
⇒ a + 3d + a + 7d = 24
⇒ 2a + 10d = 24 ⇒ a + 5d = 12
⇒ a = 12 – 5d …(1)
According to second condition, a₆ + a_10 = 44
⇒ a + 5d + a + 9d = 44
⇒ 2a + 14d = 44 ⇒ a + 7d = 22
Putting the value of a from equation (1), we get
(12 -5d) +7d = 22
⇒ 2d = 10 ⇒ d = 5
Putting the value of d in equation (1), we get a = 12 – 5(5) = – 13
The first three term of this AP: a, a + d, a + 2d = – 13, – 8, – 3.