What is the average of the first 415 natural numbers?

The average of the first 415 natural numbers

Here we will define and show you the formula and the math to calculate the average of the first 415 natural numbers.

The first 415 natural numbers are the whole numbers (integers) that start with 1 and end with 415. To make a list of the first 415 natural numbers, you simply count up to 415.

To get the average of those 415 numbers, you add them up and then divide the sum by 415. 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 = 415 in our formula, we get the average of the first 415 natural numbers. Here is the math and the answer:

avg = ((n × (n + 1)) ÷ 2) ÷ n
avg = ((415 × (415 + 1)) ÷ 2) ÷ 415
avg = ((415 × 416) ÷ 2) ÷ 415
avg = (172640 ÷ 2) ÷ 415
avg = 86320 ÷ 415
average = 208

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