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Square Pyramidal Number Calculator
To use square pyramidal Number Calculator, enter the number, and click calculate button
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 nth-term is written in mathematical form as.
Pn = {n * (n + 1) * (2n + 1)} / 6
Where,
- “Pn” is the Square number for the given nth-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, Pn =?
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, Pn =?
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,
Pn = {n * (n + 1) * (2n + 1)} / 6
P7 = {7 * (7 + 1) * (2*7 + 1)} / 6
P7 = {7*8* (15)}/ 6
P7 = 840/6
P7 = 140
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