Sum of the first 4 square numbers

We define square numbers as numbers that when squared will equal a whole number. Thus, the list of the first square numbers starts with 1, 4, 9, 16, and so on.

What is the sum of the first 4 square numbers, you ask? Here we will give you the formula to calculate the first 4 square numbers and then we will show you how to calculate the first 4 square numbers using the formula.

The formula to calculate the first n square numbers is displayed below:

		n(n + 1) × (2(n) + 1)
		6

To calculate the sum of the first 4 square numbers, we enter n = 4 into our formula to get this:

		4(4 + 1) × (2(4) + 1)
		6

First, calculate each section of the numerator: 4(4 + 1) equals 20 and (2(4) + 1) equals 9. Therefore, the problem above becomes this:

		20 × 9
		6

Next, we calculate 20 times 9 which equals 180. Now our problem looks like this:

		180
		6

Finally, divide the numerator by the denominator to get our answer:

180 ÷ 6 = 30

There you go. The sum of the first 4 square numbers is 30.

You may also be interested to know that if you list the first 4 square numbers 1, 2, 9, etc., the 4th square number is 16.

Sum of Square Numbers Calculator
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