
In an A.P., if term is n and the term is m, where m n find the 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 term of different arithmetic progressions(Aps) which is = a + (n−1)d so that we can find first and last term of AP which is required to get term.
Complete step-by-step answer:
We have the term of an AP,
For
=a+(n−1) d
Where, a is the term first term and d is the common difference
As we find term similarly we can find term
For term,
=a + (m−1) d
Where, a is the first term and d is the common difference
In the question it is given that term is equal to n
=a + (m−1)d = n ................(1)
In the question it is given that term is 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
; 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 term
=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 term
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.
Complete step-by-step answer:
We have the
For
Where, a is the
As we find
For
Where, a is the first term and d is the common difference
In the question it is given that
In the question it is given that
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
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
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
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.
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