Square Pyramidal Number Calculator

Square Pyramidal Number Calculator

Square Pyramidal Number Calculator is an online tool that finds the number of squares that are used to construct a pyramidal with a square base. 

What is the Square Pyramidal Number?

It is a positive number which shows how many squares are required to construct the square pyramidal with a square base. It is obtained by arranging square numbers in the shape of a pyramid.

Each layer of the pyramid contains a square number of objects, and the total number of objects in the pyramid can be calculated by summing up these square numbers. It is graphically shown as a regular polygonal by squares or dots.

The formula of the Square number in the n^th-term is written in mathematical form as.

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

Where,

• “P_n” is the Square number for the given n^th-term.

By continuing this process for different values of “n” we can calculate the square pyramidal numbers for higher heights of pyramids.

For example:

The first five terms in the square pyramidal Number sequence are given below.

P₁ = 1

P₂ = 5

P₃ = 14

P₄ = 30

P₅ = 55

How to evaluate the square pyramidal number?

Here are a few examples in which we find the square pyramidal numbers step-by-step.

Example 1:

Evaluate the Square number for the number “5”.

Solution:

Step 1: Write the data from the given condition.

n = 5, P_n =?

Step 2: Write the formula of the Square number.

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

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

n = 5,

P₅ = {5* (5 + 1) * (5*2 + 1)} / 6

P₅ = {5* (6) * (11)} / 6

P₅ = {5* (11)}

P5 = 55

Example 2:

Evaluate the Square number for the number “7”.

Solution:

Step 1: Write the data from the given condition.

n = 7, P_n =?

Step 2: Write the formula of the Square number.

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

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

n = 7,

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

P₇ = {7 * (7 + 1) * (2*7 + 1)} / 6

P₇ = {7*8* (15)}/ 6

P₇ = 840/6

P7 = 140