Use app×
Join Bloom Tuition
One on One Online Tuition
JEE MAIN 2025 Foundation Course
NEET 2025 Foundation Course
CLASS 12 FOUNDATION COURSE
CLASS 10 FOUNDATION COURSE
CLASS 9 FOUNDATION COURSE
CLASS 8 FOUNDATION COURSE
0 votes
265 views
in Arithmetic Progression by (24.8k points)
closed by

If mth term of an A.P. is n and nth term is m, then write its pth term.

1 Answer

+1 vote
by (27.0k points)
selected by
 
Best answer

Here, 

am = n and 

an = m 

∴ a+(m-1)d = n and a+(n-1)d = m...(1)

 Subtracting above two equation we get 

a +(m-1)d-a-(n-1)d=n-m 

∴ md - d - nd + d = n-m 

∴ d(m - n) = n - m 

∴ d = -1 

Substituting d = -1 in a+(m-1)d = n we get 

∴ a+(m-1)(-1) = n 

∴ a - m + 1 = n 

∴ a = m  +n - 1 

Now, 

pth term is given by ap = a+(p-1)d 

= m+n-1+(p-1)(-1) 

= m+n-1-p+1 

= m + n - p

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

...