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The-first-second-and-middle-terms-of-an-AP-are-a-b-c-respectively-Their-sum-is-

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Question Number 32745 by vakil vishaWakrma last updated on 01/Apr/18
The first, second and middle terms of an AP are a, b, c respectively. Their sum is
Thefirst,secondandmiddletermsofanAParea,b,crespectively.Theirsumis
Answered by Rasheed.Sindhi last updated on 01/Apr/18
Let the AP has n (odd) terms and common difference d. d=b−a The middle term=(((n+1)/2))th term=c c=a+(((n+1)/2)−1)(b−a) ((n−1)/2)=((c−a)/(b−a)) n=((2(c−a))/(b−a))+1 =((2c−2a+b−a)/(b−a)) =((−3a+b+2c)/(b−a)) Sum=(middle-term)×(number of terms) =c×n=c(((−3a+b+2c)/(b−a))) =(c/(b−a))(−3a+b+2c)
LettheAPhasn(odd)termsandcommondifferenced.d=b−aThemiddleterm=(n+12)thterm=cc=a+(n+12−1)(b−a)n−12=c−ab−an=2(c−a)b−a+1=2c−2a+b−ab−a=−3a+b+2cb−aSum=(middle−term)×(numberofterms)=c×n=c(−3a+b+2cb−a)=cb−a(−3a+b+2c)

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