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Question Number 46918 by 786786AM last updated on 02/Nov/18

Let S_n denote the sum of first n terms of an AP. If S_(2n) = 3 S_n , then the ratio (S_(3n) /S_n ) is equal to

LetSndenotethesumoffirstntermsofanAP.IfS2n=3Sn,thentheratioS3nSnisequalto

Answered by tanmay.chaudhury50@gmail.com last updated on 02/Nov/18

(s_(2n) /s_n )=((((2n)/2)[2a+(2n−1)d])/((n/2)[2a+(n−1)d]))=3 4a+(4n−2)d=6a+(3n−3)d d(4n−2−3n+3)=2a a=(((n+1)d)/2) (s_(3n) /s_n )=((((3n)/2)[2a+(3n−1)d])/((n/2)[2a+(n−1)d])) =((3[(n+1)d+(3n−1)d])/([(n+1)d+(n−1)d])) =3×((d(n+1+3n−1))/(d(n+1+n−1))) =3×((4n)/(2n))=6

s2nsn=2n2[2a+(2n−1)d]n2[2a+(n−1)d]=34a+(4n−2)d=6a+(3n−3)dd(4n−2−3n+3)=2aa=(n+1)d2s3nsn=3n2[2a+(3n−1)d]n2[2a+(n−1)d]=3[(n+1)d+(3n−1)d][(n+1)d+(n−1)d]=3×d(n+1+3n−1)d(n+1+n−1)=3×4n2n=6

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