First slide

Arithmetic progression

Question

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

Moderate

A

$\frac{α - β}{200}$
B

$α - β$
C

$\frac{α - β}{100}$
D

$β - α$

Solution

$\begin{array}{l} α = a_{2} + a_{4} + a_{6} + \dots \dots \dots \dots \dots + a_{200} \\ β = a_{1} + a_{3} + a_{5} + \dots \dots \dots . . + a_{199} \\ α - β = (a_{2} - a_{1}) + (a_{4} - a_{3}) + (a_{6} - a_{5}) + \dots \dots . . + (a_{200} - a_{199}) \\ α - β = d + d + d + \dots \dots \dots \dots . + d = 100 d \\ d = \frac{(α - β)}{100} \end{array}$

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