What is the best solution for exercise 5.2 of chapter arithmetic progressions of math, how i solve easily this question because it is very important type of question An A.P. consists of 50 terms of which 3rd term is 12 and the last term is 106. Find the 29th term.

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# An A.P. consists of 50 terms of which 3rd term is 12 and the last term is 106. Find the 29th term. Q.8

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Given that,

3

^{rd}term, a_{3}Â = 1250

^{th}term, a_{50}Â = 106We know that,

aÂ =Â_{n}a+(nâˆ’1)da_{3}Â =Âa+(3âˆ’1)d12 =Â

a+2dÂ â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦.Â(i)In the same way,

a_{50Â }=Âa+(50âˆ’1)d106 =Â

a+49dÂ â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦.Â(ii)On subtracting equationÂ

(i)Â fromÂ(ii), we get94 = 47

ddÂ = 2 = common differenceFrom equationÂ

(i), we can write now,12 =Â

a+2(2)aÂ = 12âˆ’4 = 8a_{29}Â =Âa+(29âˆ’1)Âda_{29}Â = 8+(28)2a_{29}Â = 8+56 = 64Therefore, 29

^{th}Â term is 64.