What is the average of the first 2005 natural numbers?

The average of the first 2005 natural numbers

Here we will define and show you the formula and the math to calculate the average of the first 2005 natural numbers.

The first 2005 natural numbers are the whole numbers (integers) that start with 1 and end with 2005. To make a list of the first 2005 natural numbers, you simply count up to 2005.

To get the average of those 2005 numbers, you add them up and then divide the sum by 2005. 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 = 2005 in our formula, we get the average of the first 2005 natural numbers. Here is the math and the answer:

avg = ((n × (n + 1)) ÷ 2) ÷ n
avg = ((2005 × (2005 + 1)) ÷ 2) ÷ 2005
avg = ((2005 × 2006) ÷ 2) ÷ 2005
avg = (4022030 ÷ 2) ÷ 2005
avg = 2011015 ÷ 2005
average = 1003

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What is the average of the first 2006 natural numbers?
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