Question

In an arithmetic sequence n th term is m and m th term is n. prove that its common difference is -1.

Answer 1

Data :-      

       $a_n=m\\\\a_m= n$

To prove :-

     $d=-1$

Proof :-

$a_m = a+ (m-1)d = n$ _______(1)

$a_n = a+(n-1)d = m$________(2)

On subtracting 1 and 2,

$a +(m-1) d - a - (n-1)d = n -m\\\\(m - 1 - n +1) d = n -m\\\\(m-n) d = n-m$

 

$d = \frac{- (m-n) }{m-n} \\\\=(-1)$

hope it helps u  :-)