What is the average of the first 513 natural numbers?

The average of the first 513 natural numbers

Here we will define and show you the formula and the math to calculate the average of the first 513 natural numbers.

The first 513 natural numbers are the whole numbers (integers) that start with 1 and end with 513. To make a list of the first 513 natural numbers, you simply count up to 513.

To get the average of those 513 numbers, you add them up and then divide the sum by 513. 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 = 513 in our formula, we get the average of the first 513 natural numbers. Here is the math and the answer:

avg = ((n × (n + 1)) ÷ 2) ÷ n
avg = ((513 × (513 + 1)) ÷ 2) ÷ 513
avg = ((513 × 514) ÷ 2) ÷ 513
avg = (263682 ÷ 2) ÷ 513
avg = 131841 ÷ 513
average = 257

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