What is the average of the first 684 natural numbers?

The average of the first 684 natural numbers

Here we will define and show you the formula and the math to calculate the average of the first 684 natural numbers.

The first 684 natural numbers are the whole numbers (integers) that start with 1 and end with 684. To make a list of the first 684 natural numbers, you simply count up to 684.

To get the average of those 684 numbers, you add them up and then divide the sum by 684. 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 = 684 in our formula, we get the average of the first 684 natural numbers. Here is the math and the answer:

avg = ((n × (n + 1)) ÷ 2) ÷ n
avg = ((684 × (684 + 1)) ÷ 2) ÷ 684
avg = ((684 × 685) ÷ 2) ÷ 684
avg = (468540 ÷ 2) ÷ 684
avg = 234270 ÷ 684
average = 342.5

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