Tetrahedral Pyramid Number Calculator

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.

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, 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,

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, 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,

T₇ = {7* (7 + 1) * (7 + 2)} / 6

T₇ = {7* (8) * (9)} / 6

T₇ = {56* (9)}/ 6

T₇ = 84