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Question

Let Tr be the rth term of an A.P., for r=1,2,... If for some positive integers m and n,Tm=1n;Tn=1m then find Tmn.

A
1mn
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B
1m+1n
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C
1
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D
0
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Solution

The correct option is D 1
Tm=1n (given)
a+(m1)d=1n1
Tn=1m (given)
a+(n1)d=1m2
Substract equation 2 from 1, we get
(m1)d(n1)d=1n1m
d[m1n+1]=mnmn
d[mn]=mnmn
d=1mn3
Put value of d in equation 1
a+(m1)1mn=1n
amn+(m1)mn=1n
amn+m1=m
a=1mn4
Tmn=a+(mn1)d
Tmn=1mn+(mn1)1mn (From equation 3 & 4)
Tmn=1+mn1mn=mnmn
Tmn=1

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