Q. 14.4( 60 Votes )

Show that t

Answer :

Let a and d be the first term and the common difference of the A.P. respectively.


It is known that the kth term of an A.P. is given by


ak = a + (k –1) d


am + n = a + (m + n –1) d


am – n = a + (m – n –1) d


am = a + (m –1) d


Now,


L.H.S = am + n + am – n


= a + (m + n –1) d + a + (m – n –1) d


= 2a + (m + n –1 + m – n –1) d


= 2a + (2m – 2) d


= 2a + 2 (m – 1) d


=2 [a + (m – 1) d]


= 2am


= R.H.S


Thus, the sum of (m + n)th and (m – n)th terms of an A.P. is equal to twice the mth term.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses
RELATED QUESTIONS :

There are n A.M.sRD Sharma - Mathematics

If x, y, z are inRD Sharma - Mathematics

Insert 7 A.M.s beRD Sharma - Mathematics

The 10th</suRD Sharma - Mathematics

Insert five numbeRD Sharma - Mathematics

The 4th</supRD Sharma - Mathematics

Insert 4 A.M.s beRD Sharma - Mathematics

An A.P. consists RD Sharma - Mathematics

How many terms arRS Aggarwal - Mathematics

In a cricket tourMathematics - Exemplar