Question

in an a.p if mth term is n and nth term is m, where m is not equal to n , find the pth term..?

Answer 1

I hope this answer helps you

Answer 2

The answer is given below :

Let us consider that the first term of the AP is a and the common ratio is d.

Given that,

m-th term = n

=> a + (m - 1)d = n .....(i)

and

n-th term = m

=> a + (n - 1)d = m .....(ii)

We have

a + (m - 1)d = n .....(i)
a + (n - 1)d = m .....(ii)

On subtraction, we get :

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

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

=> d = -1 [by cancelling (m - n)]

So, common ratio = -1.

Putting d = -1 in (i), we get :

a + (m - 1)(-1) = n

=> a = n + m - 1

=> a = m + n - 1

So, the first term is = m + n - 1

Hence, p-th term of the AP is

= a + (p - 1)d

= (m + n - 1) + (p - 1)(-1)

= m + n - 1 - p + 1

= m + n - p

Thank you for your question.