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Question
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.
Solution
Suppose a, a + d, a + 2d, a + 3d, ……., are in arithmetic progression, then according to the question,
∵ a4 + a8 = 24
⇒ (a + 3d) + (a + 7a) = 24
⇒ 2a + 10d = 24
⇒ a + 5d = 12 ...(1)
And a6 + a10 = 44
⇒ (a + 5a) + (a + 9d) = 44
⇒ 2a + 14d = 44
⇒ a + 7d = 22 ...(2)
⇒ 2d = 10 ...[From equation (2) – (1)]
⇒ d = `10/2`
⇒ d = 5
Putting the value of d in equation (1),
a + 5 × 5 = 12
⇒ a + 25 = 12
⇒ a = 12 – 25
⇒ a = –13
⇒ a2 = a + d
⇒ a2 = –13 + 5
⇒ a2 = –8
And a = a + 2d
a = –13 + 5 × 2
a = –13 + 10
a = –3
Hence, the required first three terms of the given arithmetic progression are –13, –8 and –3 respectively.
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