Question

if the arithmetic mean of first n natural number is 100 ,than n is​

Answer 1

Answer:

Arithmetic mean refers to the average amount in a given group of data. So arithmetic mean can be calculated by adding the first term and the last term of the series and then dividing the sum by 2. In the given series the first term is 1 and the last term is 100, so the

Arithmetic mean = ( 1+100 ) /2

= 101 /2

= 50.5

Answer 2

SOLUTION

GIVEN

The arithmetic mean of first n natural number is 100

TO DETERMINE

The value of n

EVALUATION

Here it is given that the arithmetic mean of first n natural number is 100

We know that arithmetic mean of first n natural number

$\displaystyle\sf{ = \frac{n + 1}{2} }$

So by the given condition

$\displaystyle\sf{ \frac{n + 1}{2} = 100 }$

$\displaystyle\sf{ \implies \: n + 1 = 200}$

$\displaystyle\sf{ \implies \: n = 199}$

FINAL ANSWER

Hence the required value of n = 199

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