Sum of the first 20 Square Numbers
Sum of the first 20 Square Numbers 
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Average (A) of the first 20 Square Numbers = 143.5 $$", "name": null, "url": null, "image": null, "video": null}], "name": "Final Answer", "url": null, "image": null, "video": null }]} ], "totalTime": "", "supply": "" } }
Sum of the first n natural numbers = n(n - 1)/2
Sum of the first n even numbers = n(n - 1)
Sum of the first n odd numbers = n2
Sum of the first n square numbers = n(n + 1)(2n + 1)/6
Sum of the first n cube numbers = n2(n + 1)2/4
Sum of the first n fourth power numbers = n(n + 1)(2n + 1)(3n2 + 3n - 1)/30
...,-5,-4,-3,-2,-1,0,1,2,3,4,5,...natural numberthe positive integers (whole numbers)
1, 2, 3, ...odd numbera whole number that is not able to be divided by two into two equal whole numberssumthe total amount resulting from the addition of two or more numbers, amounts, or itemssum of the first (n) numberswhole numbernumbers that include natural numbers and zero
{0, 1, 2, 3, ...}
Calculate the sum of the following
The first 20 Square Numbers
Σ n Square Numbers formula:
| S20 = | n(n + 1)(2n + 1) |
| 6 |
| S20 = | 20(20 + 1)(2(20) + 1) |
| 6 |
| S20 = | 20(21)(40 + 1) |
| 6 |
| S20 = | 20(21)(41) |
| 6 |
| S20 = | 17220 |
| 6 |
S20 = 2,870
Average (A) of the first 20 Square Numbers
| A = | Sum of the first 20 Square Numbers |
| Count |
| A = | 2870 |
| 20 |
Average (A) of the first 20 Square Numbers = 143.5
Sum of the first 20 Square Numbers
| n | Sn |
|---|---|
| 1 | 1 |
| 2 | 4 |
| 3 | 9 |
| 4 | 16 |
| 5 | 25 |
| 6 | 36 |
| 7 | 49 |
| 8 | 64 |
| 9 | 81 |
| 10 | 100 |
| 11 | 121 |
| 12 | 144 |
| 13 | 169 |
| 14 | 196 |
| 15 | 225 |
| 16 | 256 |
| 17 | 289 |
| 18 | 324 |
| 19 | 361 |
| 20 | 400 |
Final Answer
S20 = 2,870
Average (A) of the first 20 Square Numbers = 143.5
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Average (A) of the first 20 Square Numbers = 143.5 $$", "name": null, "url": null, "image": null, "video": null}], "name": "Final Answer", "url": null, "image": null, "video": null }]} ], "totalTime": "", "supply": "" } }
What is the Answer?
S20 = 2,870
Average (A) of the first 20 Square Numbers = 143.5
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)/2Sum 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 numbera whole number that is able to be divided by two into two equal whole numbersintegera whole number; a number that is not a fraction...,-5,-4,-3,-2,-1,0,1,2,3,4,5,...natural numberthe positive integers (whole numbers)
1, 2, 3, ...odd numbera whole number that is not able to be divided by two into two equal whole numberssumthe total amount resulting from the addition of two or more numbers, amounts, or itemssum of the first (n) numberswhole numbernumbers that include natural numbers and zero
{0, 1, 2, 3, ...}
Example calculations for the Sum of the First (n) Numbers Calculator
Sum of the First (n) Numbers Calculator Video
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