What is the average of the first 407 natural numbers?

The average of the first 407 natural numbers

Here we will define and show you the formula and the math to calculate the average of the first 407 natural numbers.

The first 407 natural numbers are the whole numbers (integers) that start with 1 and end with 407. To make a list of the first 407 natural numbers, you simply count up to 407.

To get the average of those 407 numbers, you add them up and then divide the sum by 407. We created a formula that can calculate the average of any sequence of natural numbers starting with 1. Here is the formula to calculate the average (avg) of the first n natural numbers:

avg = ((n × (n + 1)) ÷ 2) ÷ n

When we enter n = 407 in our formula, we get the average of the first 407 natural numbers. Here is the math and the answer:

avg = ((n × (n + 1)) ÷ 2) ÷ n
avg = ((407 × (407 + 1)) ÷ 2) ÷ 407
avg = ((407 × 408) ÷ 2) ÷ 407
avg = (166056 ÷ 2) ÷ 407
avg = 83028 ÷ 407
average = 204

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