What is the arithmetic mean of the first 100 natural numbers?
Arithmetic Mean = (Sum of Numbers) / (Number of Numbers)
In this case, the sum of the first 100 natural numbers can be found using the formula for the sum of an arithmetic series:
Sum = (n/2) * [2a + (n-1)d]
Where: n = Number of terms a = First term d = Common difference
For the first 100 natural numbers: n = 100 a = 1 (first natural number) d = 1 (common difference between natural numbers)
Now, plug these values into the formula:
Sum = (100/2) * [2(1) + (100-1)(1)] Sum = (50) * [2 + 99] Sum = 50 * 101 Sum = 5050
Now that you have the sum of the first 100 natural numbers, you can find the arithmetic mean:
Arithmetic Mean = (Sum of Numbers) / (Number of Numbers) Arithmetic Mean = 5050 / 100 Arithmetic Mean = 50.5
So, the arithmetic mean of the first 100 natural numbers is 50.5.
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