Question

The sum of the 4^th and 8^th term of an A.P. is 24 and the sum of the 6^th and 10^th term of the A.P. is 44. Find the A.P. Also, find the sum of first 25 terms of the A.P.

Answer 1

Given, a₄ + a₈ = 24

a₆ + a₁₀ = 44

Let the first term of A.P be a and common difference be d

a₄ + a₈ = 24

a + 3d + a + 7d = 24

2a + 10d = 24

a + 5d = 12  ...(1)

a₆ + a₁₀ = 44

a + 5d + a + 9d = 44

2a + 14d = 44

a + 7d = 22  ...(2)

From equation (1) and (2)

d = 5 and a = – 13

∴ First term of A.P. = – 13

and Common difference = 5

S_n = `n/2[2a + (n - 1)d]`

S₂₅ = `25/2[-26 + 24 xx 5]`

= `25/2 xx 94`

Sum of 25 terms = 25 × 47 = 1175