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

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The question is given from ncert Book of class 10th Chapter no. 5 Ex. 5.2 Q. 18. In the following question you have to find the 1st three terms of an A.P in which the sum of 4th & 8th term is 24 and sum of 6th & 10th term is 44. Give the solution.

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1. Solution:

The nth term of the AP is;

anÂ =Â a+(nâˆ’1)d

a4Â =Â a+(4âˆ’1)d

a4Â =Â a+3d

Like above, we can write,

a8Â =Â a+7d

a6Â =Â a+5d

a10Â =Â a+9d

It is given that,

a4+a8Â = 24

a+3d+a+7dÂ = 24

2a+10dÂ = 24

a+5d = 12Â  Â  Â  Â  câ€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦ (i)

a6+a10Â = 44

aÂ +5d+a+9dÂ = 44

2a+14dÂ = 44

a+7d = 22Â  Â  Â  â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦.. (ii)

By subtracting eq. (i)Â fromÂ (ii),

2d = 22 âˆ’ 12

2dÂ = 10

dÂ = 5

From eq. (i), we get,

a+5dÂ = 12

a+5(5) = 12

a+25 = 12

aÂ = âˆ’13

a2Â =Â a+dÂ = âˆ’ 13+5 = âˆ’8

a3Â =Â a2+dÂ = âˆ’ 8+5 = âˆ’3

So, the 1st three terms of the Arithmetic Progression are âˆ’13, âˆ’8, and âˆ’3.

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