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Question
The sum of the 4th and 8th term of an A.P. is 24 and the sum of the 6th and 10th term of the A.P. is 44. Find the A.P. Also, find the sum of first 25 terms of the A.P.
Solution
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
Sn = `n/2[2a + (n - 1)d]`
S25 = `25/2[-26 + 24 xx 5]`
= `25/2 xx 94`
Sum of 25 terms = 25 × 47 = 1175
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