Question

A pentagonal number is defined as n(3n−1)/2 for n=1,2,…, and so on. So, the first few numbers are 1,5,12,22,…. Write a function with the following header that returns a pentagonal number: def getPentagonalNumber(n): Write a main function that uses this function to display the first 100 pentagonal numbers with 10 numbers on each line. Use format function to display all values.

Answer 1

To write a function that returns a pentagonal number, you can use the formula n(3n-1)/2 and substitute the given value of n. Here is the implementation in Python.

Step-by-step explanation:

A pentagonal number is a number of the form n(3n-1)/2 for n = 1, 2, 3, and so on. To write a function that returns a pentagonal number, you can use the formula n(3n-1)/2 and substitute the given value of n. Here is the implementation in Python:

def getPentagonalNumber(n):
return n*(3*n-1)/2

def main():
for i in range(1, 101):
print(format(getPentagonalNumber(i), '6.0f'), end=' ')
if i % 10 == 0:
print()

main()

This function uses a loop to calculate and display the first 100 pentagonal numbers with 10 numbers on each line. The format() function is used to display the values in a specific format.

Answer 2

To display the first 100 pentagonal numbers in Python, create a function 'getPentagonalNumber' to calculate the numbers and a main function to print them in the specified format with 10 numbers per line.

Step-by-step explanation:

The subject of the question is to work with pentagonal numbers, which are figures in mathematics defined by the formula for any nth term: n(3n-1)/2.

To generate and display the first 100 pentagonal numbers in Python, we should write a function getPentagonalNumber(n) that returns the nth pentagonal number, and a main function that calls this function for the first 100 terms, formatting the output in the requested manner.

A simple Python function to calculate the nth pentagonal number could be written as:

def getPentagonalNumber(n):
return n*(3*n-1)//2

The main function that uses getPentagonalNumber to print the first 100 pentagonal numbers, organizing 10 numbers per line and using the format function for formatting, may look like this:

def main():
for i in range(1, 101):
# Call the pentagonal number function and format the output
print('{:<5}'.format(getPentagonalNumber(i)), end=' ')
# Every 10 numbers, print a new line
if i % 10 == 0:
print()

This program will print the first 100 pentagonal numbers in a neat, readable format, with properly-aligned columns.