Question

If S1, S2,S3is the sum of x,2x,3x terms respectively of an AP.Prove that S3=3(S2-S1)

Answer 1

s1=n/2[2a+(n-1)d]
s2=2n/2[2a+(2n-1)d]
s3=3n/2[2a+(3n-1)d]
therefore,
s3=3(s2-s1)
    =3{2n/2[2a+(2n-1)d]-3n/2[2a+(3n-1)d]}
=3n/2{4a+2(2n-1)d-2a-(n-1)d}
=3n/2{2a+(4n-n+1-2)}
=3n/2[2a+(3n-1)d]=s3

hope ur query gets solved by my ans......
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