Question

in an ap if tm=1/n, tn=1/ m then a -d equal to?​

Answer 1

Answer:

We can write any nth term in AP as a+(n-1)d

Where a is the first term of the series d is the difference by which each term is increasing.

So Tm (m th term) = a+(m-1)d [Solve the bracket]

=>Tm = a+md-d = 1/n [given]

Similarly Tn (n th term) =a+(n-1)d [Solve the bracket]

=>Tn = a+nd-d = 1/m [given]

We need the value of (a-d) which will obviously come in the form of m and n. So let's add the equation of Tm and Tn as we need (a-d) so we are not cancelling it hence adding the two equations.

=>Tm+Tn= a+md-d+a+nd-d = 1/m+1/n

I am attaching the further calculations. Please check the attachment for final answer.

Hope it helps...

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