First slide

Geometric progression

Question

$If the p^{th}, q^{t h}, and r^{th} terms of an A.P. are in G.P. then common ratio of the G.P is$

Moderate

A

$\frac{p r}{q^{2}}$
B

$\frac{r}{p}$
C

$\frac{q + r}{p + q}$
D

$\frac{q - r}{p - q}$

Solution

$p^{th}, q^{th}, r^{th} terms of A.P are$
$\begin{array}{l} a + (p - 1) d = x \\ a + (q - 1) d = x R \\ a + (r - 1) d = x R^{2} \\ Where R is common ratio of G.P \end{array}$
Subtracting (3) from (2) and (2) from (1) and then dividing the former
by the later, we have $\frac{q - r}{p - q} = \frac{x R^{2} - x R}{x R - x R^{2}} = R$

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