Sum of the first 7 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 7 square numbers, you ask? Here we will give you the formula to calculate the first 7 square numbers and then we will show you how to calculate the first 7 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 7 square numbers, we enter n = 7 into our formula to get this:

		7(7 + 1) × (2(7) + 1)
		6

First, calculate each section of the numerator: 7(7 + 1) equals 56 and (2(7) + 1) equals 15. Therefore, the problem above becomes this:

		56 × 15
		6

Next, we calculate 56 times 15 which equals 840. Now our problem looks like this:

		840
		6

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

840 ÷ 6 = 140

There you go. The sum of the first 7 square numbers is 140.

You may also be interested to know that if you list the first 7 square numbers 1, 2, 9, etc., the 7th square number is 49.

Sum of Square Numbers Calculator
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