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 the
a.p.

Answer 1

-13, is first term, second is -8,third term is -3, fourth term is 2

Answer 2

Answer:

We know, the nth term of the AP is;

an = a + (n − 1) d

a4 = a + (4 − 1) d

a4 = a + 3d

Thus, we can write,

a8 = a + 7d

a6 = a + 5d

a10 = a + 9d

Given in the question;

a4 + a8 = 24

a + 3d + a + 7d = 24

2a + 10d = 24

a + 5d = 12 …………………………………………………… (i)

a6 + a10 = 44

a + 5d + a + 9d = 44

2a + 14d = 44

a + 7d = 22 …………………………………….. (ii)

On subtracting equation (i) from (ii), we get,

2d = 22 − 12

2d = 10

d = 5

From equation (i), we get,

a + 5d = 12

a + 5 (5) = 12

a + 25 = 12

a = −13

a2 = a + d = − 13 + 5 = −8

a3 = a2 + d = − 8 + 5 = −3

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