The sum of the $4^{\text{th}}$ and $8^{\text{th}}$ terms of an AP is 24, and the sum of the $6^{\text{th}}$ and $10^{\text{th}}$ terms is 44. Find the first three terms of the AP.

Let $a =$ first term, $d =$ common difference.

$$t_4 + t_8 = (a + 3d) + (a + 7d)$$

$$= 2a + 10d = 24 \quad \text{...(i)}$$

$$t_6 + t_{10} = (a + 5d) + (a + 9d)$$

$$= 2a + 14d = 44 \quad \text{...(ii)}$$

Subtract (i) from (ii):

$$4d = 20 \Rightarrow d = 5$$

From (i): $2a + 50 = 24 \Rightarrow 2a = -26 \Rightarrow a = -13$.

$$t_1 = -13, t_2 = -13 + 5 = -8, t_3 = -8 + 5 = -3$$

First three terms: $-13, -8, -3$.