Question

The sam of the 4 and 8 terms of Ap is 24 and the sum of its 6 and 10 terms is 44 find the first three terms of the Ap

Answer 1

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s is 44. Find the three terms of the AP.

Ans. The sum of 4th and 8th terms of an AP is 24 and sum of 6th and 10th terms is 44.

and

Using formula , to find nth term of arithmetic progression,

a + (4 − 1) d + [a + (8 − 1) d] = 24

And, a + (6 − 1) d + [a + (10 − 1) d] = 44

⇒ a + 3d + a + 7d

= 24 And a + 5d + a + 9d = 44

⇒ 2a + 10d = 24 And 2a + 14d = 44

⇒ a + 5d = 12 And a + 7d =22

These are equations in two variables.

Using equation, a + 5d = 12, we can say that a = 12 − 5d… (1)

Putting (1) in equation a + 7d = 22,

12 − 5d + 7d = 22

⇒ 12 + 2d = 22

⇒ 2d = 10 ⇒ d = 5

Putting value of d in equation a = 12 − 5d,

a = 12 – 5 (5) = 12 – 25 = −13

Therefore, first term = a = −13 and, Common difference = d = 5

Therefore, AP is –13, –8, –3, 2…

Its first three terms are –13, –8 and –3.

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