Question

if Mth term of an AP is n and Nth term is M then find its Rth term

Answer 1

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

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 

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

Answer 2

Answer:

We have mth term=Am=a+(m-1)d=n  ..(a)

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

solving (1) and (2) we get 

(m-n)d=n-m

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

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

Step-by-step explanation: