Question

The number which should be added to the numbers $2,14,62$ so that the resulting numbers may be in G.P., is

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

The correct option is B

$2$

Explanation for the correct option

Let $x$ be the number added to $2,14,62$ , so that the resulting number may be G.P

So $\left(2+x\right),\left(14+x\right),\left(62+x\right)$ will be in G.P

Therefore, according to $b^2=ac$,

$$\begin{gathered} {\left(14+x\right)}^2=\left(2+x\right)\left(62+x\right) \\ \Rightarrow 196+28x+x^2=124+62x+2x+x^2 \\ \Rightarrow 36x=72 \\ \Rightarrow x=2 \end{gathered}$$

Hence, the correct option is $\left(\mathrm{B}\right)$