If 2x, 9 and 18 are in continued proportion, the value of x is :

1. $2\dfrac{1}{4}$

2. $\dfrac{4}{9}$

3. 1

4. 9

Given,

2x, 9 and 18 are in continued proportion.

$\therefore \dfrac{2x}{9} = \dfrac{9}{18} \\[1em] \Rightarrow x = \dfrac{9 \times 9}{18 \times 2} \\[1em] \Rightarrow x = \dfrac{9}{4} = 2\dfrac{1}{4}.$

Hence, Option 1 is the correct option.