Question

if the mean of the first n natural number is 20 then n=

Answer 1

not possible.........

Answer 2

Answer:

The value of n is 39.

Step-by-step explanation:

It is given that the mean of the first n natural number is 20.

Natural numbers are

1,2,3,4,.....

It is an AP, where a=1 and d=1.

The sum of nth terms of an AP is

$S_n=\frac{n}{2}[2a+(n-1)d]$

The sum of n natural numbers.

$S_n=\frac{n}{2}[2(1)+(n-1)(1)]$

$S_n=\frac{n}{2}[2+n-1]$

$S_n=\frac{n}{2}[1+n]$

The mean of n natural numbers is

$Mean=\frac{\text{sum of n natural numbers}}{n}$

$20=\frac{\frac{n}{2}[1+n]}{n}$

$20=\frac{1}{2}[1+n]$

$40=n+1$

$n=39$

Therefore the value of n is 39.