# Let T_r be the r^(th) term of an A.P whose first term is a and common difference is d IF for some integer m,n, T_m=1/n and T_n=1/m then a

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Let T_r be the r^(th) term of an A.P whose first term is a and common difference is d IF for some integer m,n, T_m=1/n and T_n=1/m then a-d=
A. (1)/(mn)
B. (1)/(m)+(1)/(n)
C. 1
D. 0

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Let a be the term and d be the common difference of the given AP. Then,
T_(m)=(1)/(n)rArra=(m+1)d=(1)/(n) . . . (i)
and,T_(n)=(1)/(m)rArra+(n-1)d=(1)/(m) . . . (ii)
Solving (i) and (ii), we get d=(1)/(mn)anda=(1)/(mn)
:." "T_(mn)=a+(mn-1)d=(1)/(mn-1)(1)/(mn)=1`