Question

Am = n and an = m then find ap

Answer 1

Given : Am = n and an = m

To Find :  AP

Solution:

am  = n

an =  m

Let say first term = a   and common difference = d

am = a  + (m - 1) d  = n

an = a + ( n - 1) d  = m

on subtraction :

(m - 1)d - (n - 1) d = n - m

=> (m - n) d = n - m

=> d = - 1

a  + (m - 1) d  = n

=>a  - m + 1  = n

=> a =  m + n -  1

so AP is

first term =  m + n - 1

d = - 1

m + n - 1  , m + n  - 2,  m + n - 3  , ...

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