If mth and wth terms of an A.P. be 1 and respectively, then show that

1.	If mth and wth terms of an A.P. be 1 and respectively, then show that its (mn)th term is L
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 AP 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 APA = a+(mn-1)d =1/mn+1+(-1/mn) =1 hence proved thanka

If mth and wth terms of an A.P. be 1 and respectively, then show that its (mn)th term is L

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 AP

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 APA = a+(mn-1)d =1/mn+1+(-1/mn) =1

hence proved

thanka