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The sum of 4^{th} and 8^{th} terms of an A.P. is 24 and the sum of the 6^{th} and 10^{th} terms is 44. Find the first three terms of the A.P.

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#### Solution

Suppose a, a + d, a + 2d, a + 3d,……., are in arithmetic progression, then according to the question,

∵ a_{4} + a_{8} = 24

⇒ (a + 3d) + (a + 7a) = 24

⇒ 2a + 10d = 24

⇒ a + 5d = 12 ....(1)

and a_{6} + a_{10} = 44

⇒ (a + 5a) + (a + 9d) = 44

⇒ 2a + 14d = 44

⇒ a + 7d = 22 ....(2)

⇒ 2d = 10 [from equation (2) – (1)]

⇒ d = `10/2` = 5

Putting the value of d in equation (1),

a + 5 × 5 = 12

⇒ a + 25 = 12

⇒ a = 12 - 25 = -13

⇒ a_{2} = a + d

= -13 + 5

= -8

And a = a + 2d = -13 + 5 × 2

= -13 + 10 = -3

Hence, the required first three terms of the given arithmetic progression are -13, -8 and -3 respectively.

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