Sum of the first 24 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 24 square numbers, you ask? Here we will give you the formula to calculate the first 24 square numbers and then we will show you how to calculate the first 24 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 24 square numbers, we enter n = 24 into our formula to get this:

		24(24 + 1) × (2(24) + 1)
		6

First, calculate each section of the numerator: 24(24 + 1) equals 600 and (2(24) + 1) equals 49. Therefore, the problem above becomes this:

		600 × 49
		6

Next, we calculate 600 times 49 which equals 29400. Now our problem looks like this:

		29400
		6

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

29400 ÷ 6 = 4900

There you go. The sum of the first 24 square numbers is 4900.

You may also be interested to know that if you list the first 24 square numbers 1, 2, 9, etc., the 24th square number is 576.

Sum of Square Numbers Calculator
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