What is the average of the first 214 natural numbers?

The average of the first 214 natural numbers

Here we will define and show you the formula and the math to calculate the average of the first 214 natural numbers.

The first 214 natural numbers are the whole numbers (integers) that start with 1 and end with 214. To make a list of the first 214 natural numbers, you simply count up to 214.

To get the average of those 214 numbers, you add them up and then divide the sum by 214. 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 = 214 in our formula, we get the average of the first 214 natural numbers. Here is the math and the answer:

avg = ((n × (n + 1)) ÷ 2) ÷ n
avg = ((214 × (214 + 1)) ÷ 2) ÷ 214
avg = ((214 × 215) ÷ 2) ÷ 214
avg = (46010 ÷ 2) ÷ 214
avg = 23005 ÷ 214
average = 107.5

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