The sum of the 4th and 8th terms of an AP is 24 and the sum of the 6th and 10th terms is44. Find the first three terms of the AP.

Given, a8 + a4 = 24 and a10 + a6 = 44

we know, nth term of an AP is a + (n - 1)d
where a is first term and d is common difference.
therefore,
a8 = a + 7d

a4 = a + 3d

As per question:

a + 7d + a + 3d = 24

Or, 2a + 10d = 24

Or, a + 5d = 12 …………(1)

Also,

a10 = a + 9d

a6 = a + 5d

Acc. to question :
a + 9d + a + 5d = 44

⇒ 2a + 14d = 44

⇒ a + 7d = 22..........(2)

Subtracting equation (1) from equation (2);

a + 7d – a – 5d = 22 – 12

⇒ 2d = 10

⇒ d = 5

Putting the value of d in equation (1), we get
a + 5(5) = 12
⇒ a + 25 = 12
⇒ a = -13
As, first three terms of any AP are a, a +  d, a + 2d
First three terms of given AP are -13,
-13 + 5 = -8,
-13 + 2(5) = -3.

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