Q. 14.3( 56 Votes )

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

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.
Related Videos
Interactive quiz on inequalities involving AM and GMInteractive quiz on inequalities involving AM and GMInteractive quiz on inequalities involving AM and GM45 mins
Check Your progress Part 2| Interactive Quiz: Sequence & SeriesCheck Your progress Part 2| Interactive Quiz: Sequence & SeriesCheck Your progress Part 2| Interactive Quiz: Sequence & Series47 mins
Sequence & Series (Lecture 1)Sequence & Series (Lecture 1)Sequence & Series (Lecture 1)56 mins
Sequence & Series (Lecture 5)Sequence & Series (Lecture 5)Sequence & Series (Lecture 5)42 mins
Sequence & Series (Lecture 7)Sequence & Series (Lecture 7)Sequence & Series (Lecture 7)37 mins
Trigonometric SeriesTrigonometric SeriesTrigonometric Series45 mins
Use of sigma in finding sumUse of sigma in finding sumUse of sigma in finding sum42 mins
Sequence & Series (Lecture 8)Sequence & Series (Lecture 8)Sequence & Series (Lecture 8)35 mins
Check Your progress Part 3| Interactive Quiz: Sequence & SeriesCheck Your progress Part 3| Interactive Quiz: Sequence & SeriesCheck Your progress Part 3| Interactive Quiz: Sequence & Series46 mins
Questions on relation b/w AM, GM & HMQuestions on relation b/w AM, GM & HMQuestions on relation b/w AM, GM & HM41 mins
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