What is the average of the first 2049 natural numbers?

The average of the first 2049 natural numbers

Here we will define and show you the formula and the math to calculate the average of the first 2049 natural numbers.

The first 2049 natural numbers are the whole numbers (integers) that start with 1 and end with 2049. To make a list of the first 2049 natural numbers, you simply count up to 2049.

To get the average of those 2049 numbers, you add them up and then divide the sum by 2049. 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 = 2049 in our formula, we get the average of the first 2049 natural numbers. Here is the math and the answer:

avg = ((n × (n + 1)) ÷ 2) ÷ n
avg = ((2049 × (2049 + 1)) ÷ 2) ÷ 2049
avg = ((2049 × 2050) ÷ 2) ÷ 2049
avg = (4200450 ÷ 2) ÷ 2049
avg = 2100225 ÷ 2049
average = 1025

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