What is the average of the first 1705 natural numbers?

The average of the first 1705 natural numbers

Here we will define and show you the formula and the math to calculate the average of the first 1705 natural numbers.

The first 1705 natural numbers are the whole numbers (integers) that start with 1 and end with 1705. To make a list of the first 1705 natural numbers, you simply count up to 1705.

To get the average of those 1705 numbers, you add them up and then divide the sum by 1705. 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 = 1705 in our formula, we get the average of the first 1705 natural numbers. Here is the math and the answer:

avg = ((n × (n + 1)) ÷ 2) ÷ n
avg = ((1705 × (1705 + 1)) ÷ 2) ÷ 1705
avg = ((1705 × 1706) ÷ 2) ÷ 1705
avg = (2908730 ÷ 2) ÷ 1705
avg = 1454365 ÷ 1705
average = 853

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