39th Problem

Algebra Level 2

The arithmetic mean of first 149 natural numbers is __________ \text{\_\_\_\_\_\_\_\_\_\_} .


The answer is 75.

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2 solutions

Arithmetic mean for first 149 natural numbers = 1 + 2 + 3 + . . . . . . . . + 149 149 = 149 × ( 149 + 1 ) 2 × 149 = 150 2 = 75 . \large \displaystyle \text{ Arithmetic mean for first 149 natural numbers } = \frac{1 + 2 + 3 + ........ + 149}{149}\\ \large \displaystyle = \frac{149 \times (149+1)}{2 \times 149} = \frac{150}{2} = \color{#20A900}{\boxed{75}}.

Abhiram Rao
Apr 24, 2016

Arithmetic mean of first 'n' natural numbers is = n + 1 2 \frac{n+1}{2}

Then , it will be equal to 149 + 1 2 \frac{149+1}{2} = 75

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