First slide

Geometric progression

Question

$If x, 2 x + 2, and 3 x + 3 are first three terms of a G.P. then the fourth term is$

Moderate

A

27
B

-27
C

13.5
D

-13.5

Solution

$x, 2 x + 2, 3 x + 3 are in G.P. Hence$
$\begin{array}{l} (2 x + 2)^{2} = x (3 x + 3) \\ \Rightarrow 4 x^{2} + 8 x + 4 = 3 x^{2} + 3 x \\ \Rightarrow x^{2} + 5 x + 4 = 0 \Rightarrow x = - 1, - 4 \\ So, the G.P is - 4, - 6, - 9, \dots (considering x = - 4, as for x = - 1, 2 x + 2 = 0) \end{array}$
$Hence, the fourth term is - 9 \times 1.5 = - 13.5$

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