
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
535.8k+ views
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.
Recently Updated Pages
Master Class 11 Business Studies: Engaging Questions & Answers for Success

Master Class 11 Accountancy: Engaging Questions & Answers for Success

Master Class 11 Computer Science: Engaging Questions & Answers for Success

Master Class 11 English: Engaging Questions & Answers for Success

Master Class 11 Social Science: Engaging Questions & Answers for Success

Master Class 11 Economics: Engaging Questions & Answers for Success

Trending doubts
Which one is a true fish A Jellyfish B Starfish C Dogfish class 11 biology CBSE

State and prove Bernoullis theorem class 11 physics CBSE

1 ton equals to A 100 kg B 1000 kg C 10 kg D 10000 class 11 physics CBSE

In which part of the body the blood is purified oxygenation class 11 biology CBSE

One Metric ton is equal to kg A 10000 B 1000 C 100 class 11 physics CBSE

Difference Between Prokaryotic Cells and Eukaryotic Cells
