Q. 384.2( 5 Votes )

# If the number of terms of an A.P. be 2n + 3, then find the ratio of sum of the odd terms to the sum of even terms.

Answer :

Given: Total number of terms = 2n + 3

Let the first term = a

and the common difference = d

Then, a_{k} = a + (k – 1)d …(i)

Let S_{1} and S_{2} denote the sum of all odd terms and the sum of all even terms respectively.

Then,

S_{1} = a_{1} + a_{3} + a_{5} … + a_{2n+3}

[using (i)]

= (n + 2)(a + nd + d) …(ii)

And, S_{2} = a_{2} + a_{4} + a_{6} … + a_{2n+2}

[using (i)]

= (n+1)(a + nd + d) …(iii)

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

Arithmetic progression: Previous Year NTSE Questions34 mins

Fundamental Theorem of Arithmetic- 143 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 Expertsview all courses

Dedicated counsellor for each student

24X7 Doubt Resolution

Daily Report Card

Detailed Performance Evaluation

RELATED QUESTIONS :

The sum of n terms of an A.P. is 3n^{2}+ 5n. Find the A.P. Hence, find its 16th term.