Q. 194.0( 2 Votes )

The ratio of the sums of first m and first n terms of an arithmetic series is m2: n2show that the ratio of the mth and nth terms is (2m – 1) : (2n – 1)

Answer :

Sum of m terms =

Sum of n terms =

Sum of m terms : Sum of n terms = m2 : n2

: = m2 : n2

n2m(2a + (m–1)d) = nm2( 2a + ( n–1)d)

2an2m + n2m2d – n2md = 2anm2 + n2m2d – nm2d

2anm(n–m) = nmd(n–m)

2a = d

mth term : nth term = a + (m–1)d : a + (n–1)d

mth term : nth term = a + (m–1)2a : a + (n–1) 2a

mth term : nth term = (2m–1) : (2n–1)

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:Euclid's Division Lemma44 mins
Fundamental Theorem of Arithmetic-238 mins
Fundamental Theorem of Arithmetic- 143 mins
Champ Quiz | Fundamental Principle Of Arithmetic41 mins
NCERT | Imp. Qs. on Rational and Irrational Numbers44 mins
Euclids Division Lemma49 mins
Quiz | Imp Qs on Real Numbers37 mins
Interactive Quiz - HCF and LCM32 mins
Relation Between LCM , HCF and Numbers46 mins
Application of Euclids Division Lemma50 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