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In an A.P., if mthterm is n and the nth term is m, where mn find the pth term.
A . m+n-p
B . m−n+p
C . m+n−p
D . m−n−p

Answer
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Hint:In order to solve to this problem, use general nthterm of different arithmetic progressions(Aps) which is an= a + (n−1)d so that we can find first and last term of AP which is required to get pth term.

Complete step-by-step answer:

We have the nthterm of an AP,
For
an=a+(n−1) d
Where, a is thenth term first term and d is the common difference

As we find nth term similarly we can find mth term
For mth term,
am=a + (m−1) d
Where, a is the first term and d is the common difference


In the question it is given that mthterm amis equal to n
am=a + (m−1)d = n ................(1)

In the question it is given that nthterm anis equal to m
an=a + (n−1)d = m ..............(2)

on subtracting equation (2) from equation (1),

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

On further solving
(m−1−n+1) d = n−m
(m−n)d = n−m
 d = n - mm - n
d = - 1 ; here we get common difference of AP

Substitute d = -1 in equation (1),

a+(m−1) (−1) = n
a−m+1=n
a = n+m−1; Here we get first term of AP

For pth term
ap=a+(p−1)d
On putting a= n+m−1 & d = -1 in above equation
= n+m−1+(p−1) (−1)
=n+m−1−p+1
= n+m−p ; Which is required pthterm
Hence Option C is correct.

Note: Whenever we face such type of problems we must choose expressions of nth term along with the proper understanding of common difference and first term of different APs, because by applying further proper mathematics like Addition or subtraction on general nth term we can get our desired result.