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. - Mathematics

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Sum

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.

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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` = 5

Putting the value of d in equation (1),

a + 5 × 5 = 12

⇒ a + 25 = 12

⇒ a = 12 - 25 = -13

⇒ a2 = 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.

  Is there an error in this question or solution?
Chapter 5: Arithmetic Progressions - Exercise 5.2 [Page 107]

APPEARS IN

NCERT Mathematics Class 10
Chapter 5 Arithmetic Progressions
Exercise 5.2 | Q 18 | Page 107
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