Q. 36

# If the mth term of an A.P. is and the nth term is , then prove that the sum to mn terms is , where in m n.

Given:

Now, am = a + (m – 1)d

an + n(m – 1)d = 1

an + mnd – nd = 1 …(i)

am + mnd – md = 1 …(ii)

From eq. (i) and (ii), we get

an + mnd – nd = am + mnd – md

a(n – m) –d (n – m) = 0

a = d

Now, putting the value of a in eq. (i), we get

dn + mnd – nd = 1

mnd = 1

Hence,

Sum of mn terms of AP is

Hence Proved

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Champ Quiz | Arithmetic Progression34 mins
Champ Quiz | Arithmetic Progression30 mins
Lets Check Your Knowledge in A.P.49 mins
NCERT | Fundamental Theorem Of Arithmetic45 mins
Quiz on Arithmetic Progression Quiz32 mins
Fundamental Theorem of Arithmetic- 143 mins
Arithmetic progression: Previous Year NTSE Questions34 mins
Get to Know About Geometric Progression41 mins
NCERT | Solving Questions on Introduction of A.P42 mins
Arithmetic Progression Tricks and QUIZ37 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
view all courses