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# 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. Q.18

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What are the best option for solving the problem of arithmetic progressions of exercise 5.2 of math. How i solve this problem in easy way 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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1. We know that, the nth term of the AP is;

anÂ =Â a+(nâˆ’1)d

a4Â =Â a+(4âˆ’1)d

a4Â =Â a+3d

In the same way, we can write,

a8Â =Â a+7d

a6Â =Â a+5d

a10Â =Â a+9d

Given that,

a4+a8Â = 24

a+3d+a+7dÂ = 24

2a+10dÂ = 24

a+5dÂ = 12 â€¦â€¦â€¦â€¦â€¦â€¦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+7dÂ = 22 â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦..Â (ii)

On subtracting equationÂ (i)Â fromÂ (ii), we get,

2dÂ = 22 âˆ’ 12

2dÂ = 10

dÂ = 5

From equationÂ (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

Therefore, the first three terms of this A.P. are âˆ’13, âˆ’8, and âˆ’3.

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