Question

If, S₁ is the sum of an arithmetic progression of ‘n’ odd number of terms and S₂ the sum of the terms of the series in odd places, then S₁/S₂ =

A. \(\frac{2n}{n+1}\)

B. \(\frac{n}{n+1}\)

C. \(\frac{n+1}{2n}\)

D.\(\frac{n+1}{n}\)

Answer 1

Option : (A)

Here, 

First A.P is 1,3,5… 

So, 

a =1 and d = 3-1 = 2 

Now, 

Sum of n term is given by,

Now, 

Second A.P. is 1,5,9,… 

In this A.P. a=1, d = 5-1 = 4 

Let us assume that total no. of term in first A.P. is even then total no. of term in second A.P. is \(\frac{n}{2}\).

Now,

Let us assume that total no. of term in first A.P. is odd then total no. of term in second A.P. is \(\frac{n+1}{2}\)

Now,