# Tetrahedral Pyramid Number Calculator

To use Tetrahedral Pyramid Number Calculator, enter the non-negative number, and hit the calculate button

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## Tetrahedral Pyramid Number Calculator

Tetrahedral Pyramid Number Calculator is a tool that finds the number of spheres used to construct a pyramid with a rectangular base. Its inputs are always given non-negative numbers.

## What is the Tetrahedral Pyramid Number?

It’s a positive number which shows how many spheres are required to make the pyramid with a rectangular base. It is graphically represented as a regular polygon by spheres or dots.

The formula of tetrahedral number in the nth-term is stated as.

`Tn = {n * (n + 1) * (n + 2)} / 6`

Where “Tn” is the tetrahedral number for the given nth-term.

For example:

The first five terms in the Tetrahedral Pyramid Number sequence are given as.

T1 = 1

T2 = 4

T3 = 10

T4 = 20

T5 = 35

## How to evaluate the tetrahedral number?

Example 1:

Evaluate the tetrahedral number for the number “4”.

Solution:

Step 1: Write the data from the given condition.

n = 4, Tn =?

Step 2: Write the formula of the tetrahedral number.

`Tn = {n * (n + 1) * (n + 2)} / 6`

Step 3: Put the values of “n” and evaluate for the required results.

`n = 4,`

T4 = {4* (4 + 1) * (4 + 2)} / 6

T4 = {4* (5) * (6)} / 6

T4 = {4* (5)}

`T4 = 20`

Example 2:

Evaluate the tetrahedral number for the number “7”.

Solution:

Step 1: Write the data carefully from the given condition.

n = 7, Tn =?

Step 2: Write the formula of the tetrahedral number.

`Tn = {n * (n + 1) * (n + 2)} / 6`

Step 3: Put the values of “n” and evaluate for the required results.

`n = 7,`

T7 = {7* (7 + 1) * (7 + 2)} / 6

T7 = {7* (8) * (9)} / 6

T7 = {56* (9)}/ 6

`T7 = 84`