Question

if the n term of an ap is 1 by M and m term of an ap is 1 by N prove that the mn term of an ap is 1​

Answer 1

♠♠$\huge\underline\bold{Heya!!!}$♠♠

$\huge\mathfrak\green{Solution :}$

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

$\huge\boxed{Hense\:Proved !!!}$