What is the average of the first 1640 natural numbers?

The average of the first 1640 natural numbers

Here we will define and show you the formula and the math to calculate the average of the first 1640 natural numbers.

The first 1640 natural numbers are the whole numbers (integers) that start with 1 and end with 1640. To make a list of the first 1640 natural numbers, you simply count up to 1640.

To get the average of those 1640 numbers, you add them up and then divide the sum by 1640. 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 = 1640 in our formula, we get the average of the first 1640 natural numbers. Here is the math and the answer:

avg = ((n × (n + 1)) ÷ 2) ÷ n
avg = ((1640 × (1640 + 1)) ÷ 2) ÷ 1640
avg = ((1640 × 1641) ÷ 2) ÷ 1640
avg = (2691240 ÷ 2) ÷ 1640
avg = 1345620 ÷ 1640
average = 820.5

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