Question

28. If the mth term of an A.P. be

1

n

and n

th term be

1

m

, show that its (mn)

th is 1.

Answer 1

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║║║║║║║║ ANSWER !║║║║║║║║║║║

given that, mth term=1/n and nth term=1/m.

then ,let a and d be the first term and the common difference of the A.P.

so a+(m-1)d=1/n...........(1) and a+(n-1)d=1/m...........(2).

subtracting equation (1) by (2) we get,

md-d-nd+d=1/n-1/m

=>d(m-n)=m-n/mn

=>d=1/mn.  

again if we put this value in equation (1) or (2) we get, a=1/mn.

then, let A be the mnth term of the AP

a+(mn-1)d=1/mn+1+(-1/mn)=1  

hence proved.

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