# JavaScript: Nth Tetrahedral Number

## JavaScript Math: Exercise-78 with Solution

Write a JavaScript program that takes an integer n and returns the nth Tetrahedral number.

A tetrahedral number, or triangular pyramidal number, is a figurate number that represents a pyramid with a triangular base and three sides, called a tetrahedron. The formula for the nth tetrahedral number is represented by the 3rd rising factorial of n divided by the factorial of 3:

The tetrahedral numbers are:
1, 4, 10, 20, 35, 56, 84, 120, 165, 220, ...

Test Data:
(1) -> 1
(2) -> 4
(3) -> 10
(4) -> 20
(5) -> 35

Sample Solution:

JavaScript Code:

/**
* Function to calculate the nth Tetrahedral number.
* @param {number} n - The input number.
* @returns {number} - The nth Tetrahedral number.
*/
function test(n) {
// Calculate the Tetrahedral number using the formula (n * (n + 1) * (n + 2)) / 6
return n * (n + 1) * (n + 2) / 6;
}

// Test cases
// Assign value to n
n = 1;
// Print n
console.log("n = " + n);
// Print nth Tetrahedral number
console.log("nth Tetrahedral number = " + test(n));
// Repeat the above steps for different values of n
n = 2;
console.log("n = " + n);
console.log("nth Tetrahedral number = " + test(n));
n = 3;
console.log("n = " + n);
console.log("nth Tetrahedral number = " + test(n));
n = 4;
console.log("n = " + n);
console.log("nth Tetrahedral number = " + test(n));
n = 5;
console.log("n = " + n);
console.log("nth Tetrahedral number = " + test(n));

Output:

n = 1
nth Tetrahedral number = 1
n = 2
nth Tetrahedral number = 4
n = 3
nth Tetrahedral number = 10
n = 4
nth Tetrahedral number = 20
n = 5
nth Tetrahedral number = 35

Flowchart:

Live Demo:

See the Pen javascript-math-exercise-78 by w3resource (@w3resource) on CodePen.

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