First slide

Arithmetic progression

Question

The first and last terms of an A.P. are a and l respectively. If s is the sum of all the terms of the A.P., then the common difference of the A.P. is

Moderate

A

$\frac{l^{2} - a^{2}}{s - (l + a)}$
B

$\frac{l^{2} - a^{2}}{2 s - (l + a)}$
C

$\frac{l^{2} + a^{2}}{2 s - (l + a)}$
D

$\frac{l^{2} + a^{2}}{s - (l - a)}$

Solution

Let n be the number of terms. Then
$s = \frac{n}{2} (a + l) \Rightarrow n = \frac{2 s}{a + l}$
Also,
$d = \frac{l - a}{n - 1} = \frac{(l - a) (l + a)}{2 s - (l + a)} = \frac{l^{2} - a^{2}}{2 s - (l + a)}$

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