The G.M. of the numbers 3, 3^2, 3^3, ..., 3^n | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) The Geometric Mean $(G.M.)$ of $n$ numbers $x_1, x_2, ..., x_n$ is given by $(x_1 \cdot x_2 \cdot ... \cdot x_n)^{1/n}$.Here,the numbers are $3^1,

Vedclass · Accepted Answer

$3^{\frac{n+1}{2}}$

Vedclass · Answer

(B) The Geometric Mean $(G.M.)$ of $n$ numbers $x_1, x_2, ..., x_n$ is given by $(x_1 \cdot x_2 \cdot ... \cdot x_n)^{1/n}$.Here,the numbers are $3^1, 3^2, 3^3, ..., 3^n$.$G.M. = (3^1 \cdot 3^2 \cdot 3^3 \cdot ... \cdot 3^n)^{1/n}$Using the property of exponents,$a^m \cdot a^n = a^{m+n}$,we get:$G.M. = (3^{1+2+3+...+n})^{1/n}$The sum of the first $n$ natural numbers is $\frac{n(n+1)}{2}$.$G.M. = (3^{\frac{n(n+1)}{2}})^{1/n}$$G.M. = 3^{\frac{n(n+1)}{2} \cdot \frac{1}{n}}$$G.M. = 3^{\frac{n+1}{2}}$.

The $G.M.$ of the numbers $3, 3^2, 3^3, ..., 3^n$ is

Similar Questions

If $y = x - x^2 + x^3 - x^4 + \dots \infty$,then the value of $x$ will be

If $y = x + x^2 + x^3 + \dots \infty$,then $x = $

If $H$ is the harmonic mean between $p$ and $q$,then the value of $\frac{H}{p} + \frac{H}{q}$ is

Let $a, b$ and $c$ be the $7^{th}, 11^{th}$ and $13^{th}$ terms respectively of a non-constant $A.P.$ If these are also the three consecutive terms of a $G.P.$,then $\frac{a}{c}$ is equal to

Determine $k$ so that $\frac{2}{3}, k$ and $\frac{5}{8} k$ are the three consecutive terms of an $A.P.$

Vedclass Test Series

Exam Paper Generator

Online Exam Module