# Sum of the first 10 Square Numbers

## Enter n:

Sum of the First

Calculate the sum of the following
The first 10 Square Numbers

## Σ n Square Numbers formula:

 S10  = n(n + 1)(2n + 1) 6

 S10  = 10(10 + 1)(2(10) + 1) 6

 S10  = 10(11)(20 + 1) 6

 S10  = 10(11)(21) 6

 S10  = 2310 6

S10 = 385

## Average (A) of the first 10 Square Numbers

 A  = Sum of the first 10 Square Numbers Count

 A  = 385 10

Average (A) of the first 10 Square Numbers = 38.5

## Sum of the first 10 Square Numbers

n    Sn
1    1
2    4
3    9
4    16
5    25
6    36
7    49
8    64
9    81
10    100

S10 = 385
Average (A) of the first 10 Square Numbers = 38.5

### How does the Sum of the First (n) Numbers Calculator work?

Free Sum of the First (n) Numbers Calculator - Determines the sum of the first (n)
* Whole Numbers
* Natural Numbers
* Even Numbers
* Odd Numbers
* Square Numbers
* Cube Numbers
* Fourth Power Numbers
This calculator has 1 input.

### What 7 formulas are used for the Sum of the First (n) Numbers Calculator?

Sum of the first n whole numbers = n(n - 1)/2
Sum of the first n natural numbers = n(n - 1)/2
Sum of the first n even numbers = n(n - 1)
Sum of the first n odd numbers = n2
Sum of the first n square numbers = n(n + 1)(2n + 1)/6
Sum of the first n cube numbers = n2(n + 1)2/4
Sum of the first n fourth power numbers = n(n + 1)(2n + 1)(3n2 + 3n - 1)/30

For more math formulas, check out our Formula Dossier

### What 7 concepts are covered in the Sum of the First (n) Numbers Calculator?

even number
a whole number that is able to be divided by two into two equal whole numbers
integer
a whole number; a number that is not a fraction
...,-5,-4,-3,-2,-1,0,1,2,3,4,5,...
natural number
the positive integers (whole numbers)
1, 2, 3, ...
odd number
a whole number that is not able to be divided by two into two equal whole numbers
sum
the total amount resulting from the addition of two or more numbers, amounts, or items
sum of the first (n) numbers
whole number
numbers that include natural numbers and zero
{0, 1, 2, 3, ...}