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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# 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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We know that, the nth term of the AP is;

aÂ =Â_{n}a+(nâˆ’1)da_{4}Â =Âa+(4âˆ’1)da_{4}Â =Âa+3dIn the same way, we can write,

a_{8}Â =Âa+7da_{6}Â =Âa+5da_{10}Â =Âa+9dGiven that,

a

_{4}+a_{8}Â = 24a+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)a

_{6}+a_{10}Â = 44aÂ +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 = 5From equationÂ

(i), we get,a+5dÂ = 12a+5(5) = 12a+25 = 12aÂ = âˆ’13a_{2}Â =Âa+dÂ = âˆ’ 13+5 = âˆ’8a_{3}Â =Âa_{2}+dÂ = âˆ’ 8+5 = âˆ’3Therefore, the first three terms of this A.P. are âˆ’13, âˆ’8, and âˆ’3.