What is the average of the first 198 natural numbers?

The average of the first 198 natural numbers

Here we will define and show you the formula and the math to calculate the average of the first 198 natural numbers.

The first 198 natural numbers are the whole numbers (integers) that start with 1 and end with 198. To make a list of the first 198 natural numbers, you simply count up to 198.

To get the average of those 198 numbers, you add them up and then divide the sum by 198. 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 = 198 in our formula, we get the average of the first 198 natural numbers. Here is the math and the answer:

avg = ((n × (n + 1)) ÷ 2) ÷ n
avg = ((198 × (198 + 1)) ÷ 2) ÷ 198
avg = ((198 × 199) ÷ 2) ÷ 198
avg = (39402 ÷ 2) ÷ 198
avg = 19701 ÷ 198
average = 99.5

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What is the average of the first 199 natural numbers?
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