Question

find the common ratio of GP 2 2 root 2 4 .......​

Answer 1

Answer:

The common ratio is $\sqrt2$

Step-by-step explanation:

Concept:

The common ratio of the G.P

$a,\:ar\,\:ar^2...........$ is given by

$r=\frac{t_2}{t_1}=\frac{t_3}{t_2}=\frac{t_4}{t_3}=\frac{t_5}{t_4}=.......$

Given G.P is

$2,\:2\sqrt2,\:4...........$

Then,

$\text{ common ratio }r=\frac{t_2}{t_1}$

$\text{ common ratio,}r=\frac{2\sqrt2}{2}$

$\implies\text{ common ratio,}\bf\:r=\sqrt2}$

Answer 2

Given:

G.P

2,$2\sqrt{2},4...$

To find:

Common ratio of G.P

Solution:

$a_1=2$

$a_2=2\sqrt{2}$

$a_3=4$

We know that

Common ratio of G.P,r=$\frac{a_2}{a_1}$

Using the formula

$r=\frac{2\sqrt{2}}{2}$

$r=\frac{2\times \sqrt{2}}{2}$

$r=\sqrt{2}$

Hence, the common ratio of GP=$\sqrt{2}$