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
1.1k views
in Arithmetic Progression by (22.8k points)
closed by

Let Tr be the rth term of an A.P. whose first term is a and the common difference is d. If for some positive integers m and n, Tm\(\frac{1}{n}\) and Tn\(\frac{1}{m}\), then (a – d) equals

(a) 1/mn 

(b) 1 

(c) 0 

(d) \(\frac{1}{m}\) + \(\frac{1}{n}\)

1 Answer

+1 vote
by (23.7k points)
selected by
 
Best answer

Answer : (c) 0

Given, 

Tm\(\frac{1}{n}\) ⇒ a + (m-1)d = \(\frac{1}{n}\)  ...(i)

Tn\(\frac{1}{m}\) ⇒ a + (n-1)d = \(\frac{1}{m}\) ... (ii)

Eq. (ii) – Eq. (i) 

⇒ (n – m)d = \(\frac{1}{m}\) - \(\frac{1}{n}\)

⇒ (n - m)d = \(\frac{n-m}{mn}\) 

⇒ d = \(\frac{1}{mn}\)

Putting d = \(\frac{1}{mn}\) in (i), we get a = \(\frac{1}{mn}\)

∴ a – d = \(\frac{1}{mn}\) - \(\frac{1}{mn}\) = 0

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.

...