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In an AP , if Mth term is n and Nth term is m ,where M is not equal to N, find the Pth term..

In an AP , if Mth term is n and Nth term is m ,where M is not equal to N, find the Pth term..

Grade:11

2 Answers

Adhiraj Mandal
32 Points
9 years ago

Dear Vishal,

The m-th term is a+(m-1)d=n and the n-th term is a+(n-1)d=m

Therefore,a+md-d=n and a+nd-d=m

Subtracting the second result from the first result we get

a+md-d-a-nd+d=n-m

this implies,(m-n) d=(n-m)

therefore,d=(-1)

Therefore the p-th term is a+(p-1)d=a+(p-1)(-1)=a-p+1

I Hope I have come to your help.

With Regards,ADHIRAJ

Aâkäsh Kùmãr Pândéý
44 Points
5 years ago
We have am= a+(m-1)d=n........(1) and an= a+(n-1)d=m........(2)Solving (1) & (2), we get (m-n)d= n-m, or d= -1,And a=n+m-1Therefore ap = a+(p-1)d =n+m-1+(p-1) (-1)= n+m-pHence, the pth term is n+m-p.

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