Question

7th term of the sequence$\sqrt{2}$,$\sqrt{10}$,$5\sqrt{2}$….is

• A. $125\sqrt{10}$
• B. $25\sqrt{2}$
• C. $125$
• D. $125\sqrt{2}$

Answer 1

The correct option is D

$125\sqrt{2}$

Explanation for the correct option:

Step1: Recognise the pattern in sequence:

We have the following sequence$\sqrt{2}$,$\sqrt{10}$,$5\sqrt{2}$

Here,

$\frac{\sqrt{10}}{\sqrt{2}}=\sqrt{5}=\frac{5\sqrt{2}}{\sqrt{10}}$

So, we can say sequence is geometric progression.

We have First Term$=a=\sqrt{2}$

Common Ratio $=r=\sqrt{5}$

Step2: 7th term of the progression:

$n^{th}$ term of GP$\mathbf{=}{\mathbf{ar}}^{\mathbf{n}\mathbf{-}\mathbf{1}}$

So, $7^{th}term=\sqrt{2}\times {\left(\sqrt{5}\right)}^6$

$=125\sqrt{2}$

Hence, option(D) is correct.