The sixth H.M. between 3 and frac{6}{13} is | vedclass

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

Question

(A) The formula for the $n^{th}$ Harmonic Mean $(H.M.)$ between two numbers $a$ and $b$ is given by $H_n = \frac{(n+1)ab}{na+b}$.Here,$a = 3$,$b = \fr

Vedclass · Accepted Answer

$\frac{63}{120}$

Vedclass · Answer

(A) The formula for the $n^{th}$ Harmonic Mean $(H.M.)$ between two numbers $a$ and $b$ is given by $H_n = \frac{(n+1)ab}{na+b}$.Here,$a = 3$,$b = \frac{6}{13}$,and $n = 6$.Substituting these values into the formula:$H_6 = \frac{(6+1) 	imes 3 	imes \frac{6}{13}}{6 	imes 3 + \frac{6}{13}}$$H_6 = \frac{7 	imes 3 	imes \frac{6}{13}}{18 + \frac{6}{13}}$$H_6 = \frac{\frac{126}{13}}{\frac{234+6}{13}}$$H_6 = \frac{126}{240}$Simplifying the fraction by dividing both numerator and denominator by $2$,we get:$H_6 = \frac{63}{120}$.

The sixth $H.M.$ between $3$ and $\frac{6}{13}$ is

Similar Questions

Let $a_1, a_2, ......., a_{30}$ be an $A.P.$,$S = \sum_{i=1}^{30} a_i$ and $T = \sum_{i=1}^{15} a_{2i-1}$. If $a_5 = 27$ and $S - 2T = 75$,then $a_{10}$ is equal to

If $p$ times the $p^{th}$ term of an $A.P.$ is equal to $q$ times the $q^{th}$ term of an $A.P.$,then the $(p + q)^{th}$ term is

The roots of the equation $x^5 - 40x^4 + px^3 + qx^2 + rx + s = 0$ are in $G.P.$ The sum of their reciprocals is $10$. Then the value of $|s|$ is

If $n$ geometric means are inserted between $a$ and $b$,then the $n^{th}$ geometric mean will be:

The sum of $100$ terms of the series $0.9 + 0.09 + 0.009 + \dots$ will be

Vedclass Test Series

Exam Paper Generator

Online Exam Module