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Question

If the ratio of sum of m terms and n terms of an A.P. be m2:n2, then the ratio of its mth and nth terms will be

A
2m-1 : 2n-1
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B
m:n
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C
2m+1 : 2n+1
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D
None
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Solution

The correct option is D 2m-1 : 2n-1
By using Sn=n2[2a+(n1)d] we have

Given that m2[2a+(m1)d]n2[2a+(n1)d]=m2n2

2a+(m1)d2a+(n1)d=mn
a+12(m1)da+12(n1)d=mn

an+12(m1)dn=am+12(n1)md

a(nm)+d2[mnnmn+m]=0

a(nm)+d2(mn)=0

a=d2 or d=2a

Therefore, TmTn=a+(m1)da+(n1)d

=a+(m1)2aa+(n1)2a

=1+2m21+2n2

=2m12n1

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