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Let Tr be the rth term of an A.P., for r...

Let `T_r` be the rth term of an A.P., for `r=1,2,3,` If for some positive integers `m ,n ,` we have `T_m=1/na n dT_n=1/m ,t h e nT_(m n)` equals `1/(m n)`

A

`(1)/(mn)`

B

`(1)/(m) + (1)/(n)`

C

1

D

0

Text Solution

Verified by Experts

The correct Answer is:
C
Let `T_(m) = a + (m-1) d = (1)/(n)` ....(i)
and `T_(n) = a+(n -1) d = (1)/(m)`..(ii)
On subtracting Eq. (ii) from Eq. (i), we get
`(m -n) d = (1)/(n) - (1)/(m) = (m-n)/(mn)`
`rArr d = (1)/(mn)`
Again, `T_(mn) = a + (mn -1) d = a + (mn - n + n -1) d`
`= a + (n -1) d + (mn -n) d`
`= T_(n) + n (m-1) (1)/(mn) = (1)/(m) + ((m-1))/(m) = 1`
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