#### Question

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

#### Solution

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

Given that, a_{4} + a_{8} = 24

a + 3d + a + 7d = 24

2a + 10d = 24

a + 5d = 12 (1)

a_{6} + a_{10} = 44

a + 5d + a + 9d = 44

2a + 14d = 44

a + 7d = 22 (2)

On subtracting equation (1) from (2), we obtain

2d = 22 − 12

2d = 10

d = 5

From equation (1), we obtain

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

Therefore, the first three terms of this A.P. are −13, −8, and −3.

Is there an error in this question or solution?

Solution The sum of 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 the A.P. Concept: nth Term of an AP.