Question

the sum of the 4th and 8th terms of an ap is 24 and sum of 6th and 10th term is 44. Find the sum of frist 10 th terms of the Ap

Answer 1

4th term + 8th term = 24

=> a + 3d + a + 7d = 24

=> 2a + 10d = 24

=> a + 5d = 12 ..........................eq.(1)

6th term + 10th term = 44

=> a + 5d + a + 9d = 44

=> 2a + 14d = 44

=> a + 7d = 22 ..................eq.(2)

solving eq. 1 and 2

a + 5d = 12

a + 7d = 22

-----------------

- 2d = -10

d = 5

then from eq(1)

a = 12 - 5x5

= 12 - 25

= -13

$S10 = \frac{10}{2} (2 \times ( - 13) + 9 \times 5) \\ = 5( - 26 + 45) \\ = 5 \times 19 \\ = 95$