Q. 18

# If there are (2n + 1) terms in an arithmetic series, then prove that the ratio of the sum of odd terms to the sum of even terms is (n + 1) : n.

In the A.P, let

First term = a

Common difference = d

Number of terms = (2n + 1)

Series: a,a + d,a + 2d……a + 2nd

For Odd terms

: a, a + 2d,…a + 2nd

First term = a

Common difference = 2d

Number of terms = n + 1

Sum of terms = Sum of odd terms = Sum of odd terms = For Even terms

: a + d, a + 3d,…a + (2n–1)d

First term = a + d

Common difference = 2d

Number of terms = n

Sum of terms = Sum of even terms = Sum of even terms = Sum of odd terms : Sum of even terms = : = Sum of odd terms : Sum of even terms = (n + 1) : n

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  Champ Quiz | Fundamental Principle Of Arithmetic41 mins  Euclids Division Lemma49 mins  Fundamental Theorem of Arithmetic- 143 mins  Quiz | Imp Qs on Real Numbers37 mins  NCERT | Imp. Qs. on Rational and Irrational Numbers44 mins  Application of Euclids Division Lemma50 mins  Relation Between LCM , HCF and Numbers46 mins  Quiz | Fun with Fundamental Theorem of Arithmetic51 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 