First slide

Arithmetic progression

Question

Let $a_{n}$ be the $n t h$ term of an A.P. If $\sum_{r = 1}^{100} a_{2 r} = α$ and $\sum_{r = 1}^{100} a_{2 r - 1} = β$ , then the common difference of the A.P. is:

Moderate

A

$α - β$
B

$\frac{1}{100} (α - β)$
C

$β - α$
D

$\frac{1}{200} (α - β)$

Solution

Let $d$ the common difference of the A.P., then
$\begin{array}{l} α - β = \sum_{r = 1}^{100} (a_{2 r} - a_{2 r - 1}) = \sum_{r = 1}^{100} d = 100 d \\ \Rightarrow d = \frac{1}{100} (α - β) \end{array}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App