Question

Geometric mean of $7,7^2,7^3,...,7^n$ is

• A. ${\left(7\right)}^{\frac{(n+1)}{2}}$
• B. $7$
• C. ${\left(7\right)}^{\frac{n}{2}}$
• D. $7^n$

Answer 1

The correct option is A

${\left(7\right)}^{\frac{(n+1)}{2}}$

Explanation for the correct option:

Find the geometric mean:

$\because$Geometric mean of two numbers $a$ and $b$ $=\sqrt{\mathbf{a}\mathbf{b}}$

⇒ For a GP, Geometric mean $=\sqrt{a_1.a_n}$

⇒ Geometric mean of $7,7^2,7^3,...,7^n$ $=\sqrt{7.7^n}$

$=\sqrt{7^{n+1}}$

$={\left(7\right)}^{\frac{\mathbf{n}\mathbf{+}\mathbf{1}}{\mathbf{2}}}$

Hence, Option ‘A’ is Correct.