What is the average of the first 406 natural numbers?

The average of the first 406 natural numbers

Here we will define and show you the formula and the math to calculate the average of the first 406 natural numbers.

The first 406 natural numbers are the whole numbers (integers) that start with 1 and end with 406. To make a list of the first 406 natural numbers, you simply count up to 406.

To get the average of those 406 numbers, you add them up and then divide the sum by 406. 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 = 406 in our formula, we get the average of the first 406 natural numbers. Here is the math and the answer:

avg = ((n × (n + 1)) ÷ 2) ÷ n
avg = ((406 × (406 + 1)) ÷ 2) ÷ 406
avg = ((406 × 407) ÷ 2) ÷ 406
avg = (165242 ÷ 2) ÷ 406
avg = 82621 ÷ 406
average = 203.5

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