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# Tetrahedral Pyramid Number Calculator

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

## Tetrahedral Pyramid Number Calculator

Tetrahedral Pyramid Number Calculator is a tool that finds the number of spheres which 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 n^{th}-term is stated as.

**T _{n} = {n **

*** (n + 1)**

*** (n + 2)} / 6**

Where “**T _{n}**” is the tetrahedral number for the given n

^{th}-term.

**For example:**

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

T_{1} = 1

T_{2} = 4

T_{3} = 10

T_{4} = 20

T_{5} = 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, T_{n} =?

**Step 2:**

Write the formula of the tetrahedral number.

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

**Step 3:**

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

n = 4,

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

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

T_{4} = {4* (5)}

T_{4} = 20

**Example 2:**

Evaluate the tetrahedral number for the number “7”.

**Solution:**

**Step 1:**

Write the data carefully from the given condition.

n = 7, T_{n} =?

**Step 2:**

Write the formula of the tetrahedral number.

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

**Step 3:**

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

n = 7,

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

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

T_{7} = {56* (9)}/ 6

T_{7} = 84