The average of the first 199 natural numbers
Here we will define and show you the formula and the math to calculate the average of the first 199 natural numbers.
The first 199 natural numbers are the whole numbers (integers) that start with 1 and end with 199. To make a list of the first 199 natural numbers, you simply count up to 199.
To get the average of those 199 numbers, you add them up and then divide the sum by 199. 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 = 199 in our formula, we get the average of the first 199 natural numbers. Here is the math and the answer:
avg = ((n × (n + 1)) ÷ 2) ÷ n
avg = ((199 × (199 + 1)) ÷ 2) ÷ 199
avg = ((199 × 200) ÷ 2) ÷ 199
avg = (39800 ÷ 2) ÷ 199
avg = 19900 ÷ 199
average = 100
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