What is the average of the first 1609 natural numbers?

The average of the first 1609 natural numbers

Here we will define and show you the formula and the math to calculate the average of the first 1609 natural numbers.

The first 1609 natural numbers are the whole numbers (integers) that start with 1 and end with 1609. To make a list of the first 1609 natural numbers, you simply count up to 1609.

To get the average of those 1609 numbers, you add them up and then divide the sum by 1609. 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 = 1609 in our formula, we get the average of the first 1609 natural numbers. Here is the math and the answer:

avg = ((n × (n + 1)) ÷ 2) ÷ n
avg = ((1609 × (1609 + 1)) ÷ 2) ÷ 1609
avg = ((1609 × 1610) ÷ 2) ÷ 1609
avg = (2590490 ÷ 2) ÷ 1609
avg = 1295245 ÷ 1609
average = 805

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