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The sum of the 4th and 8th terms of an AP is 24 and the sum of

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The sum of the 4th and 8th terms of an AP is 24 and the sum of the 6th and 10th terms is 44. Find the first three terms of the AP.

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Text solutionVerified

Solution: Here, we are given,

a_{4} + a_{8} = 24 \Rightarrow a + 3 d + a + 7 d = 24

2 a + 10 d = 24

a + 5 d = 12 \to E q (1)

a_{6} + a_{10} = 24 \Rightarrow a + 5 d + a + 9 d = 44

2 a + 14 d = 44

a + 7 d = 22 \to E q (2)

Subtracting (1) from (2),

2 d = 10 \Rightarrow d = 5

Putting value of d in (1),

a + 5 (5) = 12 \Rightarrow a = - 13

So, first three terms of AP are

- 13, - 8, - 3

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Question Text	The sum of the 4th and 8th terms of an AP is 24 and the sum of the 6th and 10th terms is 44. Find the first three terms of the AP.
Answer Type	Text solution:1
Upvotes	150