What is the average of the first 1600 natural numbers?

The average of the first 1600 natural numbers

Here we will define and show you the formula and the math to calculate the average of the first 1600 natural numbers.

The first 1600 natural numbers are the whole numbers (integers) that start with 1 and end with 1600. To make a list of the first 1600 natural numbers, you simply count up to 1600.

To get the average of those 1600 numbers, you add them up and then divide the sum by 1600. 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 = 1600 in our formula, we get the average of the first 1600 natural numbers. Here is the math and the answer:

avg = ((n × (n + 1)) ÷ 2) ÷ n
avg = ((1600 × (1600 + 1)) ÷ 2) ÷ 1600
avg = ((1600 × 1601) ÷ 2) ÷ 1600
avg = (2561600 ÷ 2) ÷ 1600
avg = 1280800 ÷ 1600
average = 800.5

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