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**If S1 is the sum of an arithmetic progression of ‘n’ odd number of terms and S2 is the sum of the terms of the series in odd places, then $\frac{S_{1}}{S_{2}}$.**

A. $\frac{2 n}{n+1}$
B. $\frac{n}{n+1}$
C. $\frac{n+1}{2 n}$
D. $\frac{n-1}{n}$
**Answer: Option A**

## Show Answer

Solution(By Apex Team)

Odd numbers are 1, 3, 5, 7, 9, 11, 13, …… n
∴ S1 = Sum of odd numbers = n2
S2 = Sum of number at odd places
3, 7, 11, 15, ……
a = 3, d = 7 – 3 = 4 and number of term = $\Large\frac{n}{2}$
$\begin{aligned}S_2&=\frac{n}{2\times2}\left[2\times3+\left(\frac{n}{2}-1\right)\times4\right]\\
&=\frac{n}{4}[6+2n-4]\\
&=\frac{n}{4}[2n+2]\\
&=\frac{n(n+1)}{2}\\
\therefore&\frac{s_1}{s_2}=\frac{n^2\times2}{n(n+1)}\\
&=\frac{2n}{n+1}\end{aligned}$

## Related Questions On Progressions

### How many terms are there in 20, 25, 30 . . . . . . 140?

A. 22B. 25

C. 23

D. 24

### Find the first term of an AP whose 8th and 12th terms are respectively 39 and 59.

A. 5B. 6

C. 4

D. 3

### Find the 15th term of the sequence 20, 15, 10 . . .

A. -45B. -55

C. -50

D. 0

### The sum of the first 16 terms of an AP whose first term and third term are 5 and 15 respectively is

A. 600B. 765

C. 640

D. 680