Question

average of first n natural number is 84 then what is the average of 3n natural number?​

Answer 1

Answer:

125751

Step-by-step explanation:

Attached in above Image

Answer 2

The average of 3n natural numbers is 251.

Step-by-step explanation:

Sum of first n natural numbers = $\frac{n(n+1)}{2}$

Average of first n natural numbers = $\frac{n(n+1)}{2n}=\frac{n+1}{2}$

Given, average of first n natural numbers is 84.

$\frac{n+1}{2}=84$

=> n + 1 = 84 x 2 = 168

=> n = 168 - 1 = 167

Sum of first 3n natural numbers = $\frac{3n(3n+1)}{2}$

Average of first 3n natural numbers = $\frac{3n(3n+1)}{2\times 3n}=\frac{3n+1}{2}$

Plug the value of n = 167

$\frac{3n+1}{2} \\= \frac{3\times167+1}{2}\\= \frac{502}{2}\\= 251$

Hence, the average of 3n natural numbers is 251.