Question

in an ap..if mth term is n and nth term is m,show that its rth term is (m+n-r)

Answer 1

We have mth
term=Am=a+(m-1)d=n..................(1) 


we have
nth term=An=a+(n-1)d=m......................... (2)

solving (1) and (2) we will get 

(m-n)d=n-m 

that is,d=(n-m)/-(n-m) (since m-n= -(n-m) ) 
or,d=-1 

and a=n+m-1 

rth term = a+(r-1)-1 =n+m-1+(r-1)-1 
So,
rth term is m+n-r


Hope it was helpful ^_^