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Python: Check whether a given sequence is linear, quadratic or cubic

Python Basic - 1: Exercise-105 with Solution

Write a Python program to check whether a given sequence is linear, quadratic or cubic.

Sequences are sets of numbers that are connected in some way.
Linear sequence:
A number pattern which increases or decreases by the same amount each time is called a linear sequence. The amount it increases or decreases by is known as the common difference.
Quadratic sequence:
In quadratic sequence, the difference between each term increases, or decreases, at a constant rate.
Cubic sequence:
Sequences where the 3rd difference are known as cubic sequence.

Sample Solution:

Python Code:

def Seq_Linear_Quadratic_Cubic(seq_nums):
  seq_nums = [seq_nums[x] - seq_nums[x-1] for x in range(1, len(seq_nums))]
  if len(set(seq_nums)) == 1: return "Linear Sequence"
  seq_nums = [seq_nums[x] - seq_nums[x-1] for x in range(1, len(seq_nums))]
  if len(set(seq_nums)) == 1: return "Quadratic Sequence"
  seq_nums = [seq_nums[x] - seq_nums[x-1] for x in range(1, len(seq_nums))]
  if len(set(seq_nums)) == 1: return "Cubic Sequence"

nums = [0,2,4,6,8,10]
print("Original Sequence:",nums)
print("Check the said sequence is Linear, Quadratic or Cubic?")
print(Seq_Linear_Quadratic_Cubic(nums))
nums = [1,4,9,16,25]
print("\nOriginal Sequence:",nums)
print("Check the said sequence is Linear, Quadratic or Cubic?")
print(Seq_Linear_Quadratic_Cubic(nums))
nums = [0,12,10,0,-12,-20]
print("\nOriginal Sequence:",nums)
print("Check the said sequence is Linear, Quadratic or Cubic?")
print(Seq_Linear_Quadratic_Cubic(nums))
nums = [1,2,3,4,5]
print("\nOriginal Sequence:",nums)
print("Check the said sequence is Linear, Quadratic or Cubic?")
print(Seq_Linear_Quadratic_Cubic(nums))

Sample Output:

Original Sequence: [0, 2, 4, 6, 8, 10]
Check the said sequence is Linear, Quadratic or Cubic?
Linear Sequence

Original Sequence: [1, 4, 9, 16, 25]
Check the said sequence is Linear, Quadratic or Cubic?
Quadratic Sequence

Original Sequence: [0, 12, 10, 0, -12, -20]
Check the said sequence is Linear, Quadratic or Cubic?
Cubic Sequence

Original Sequence: [1, 2, 3, 4, 5]
Check the said sequence is Linear, Quadratic or Cubic?
Linear Sequence

Flowchart:

Flowchart: Python - Check whether a given sequence is linear, quadratic or cubic.

Python Code Editor:

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Previous: Write a Python program to find a number in a given matrix, which is maximum in its column and minimum in its row.
Next: Write a Python program to test whether a given integer is Pandigital number or not.

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Python: Tips of the Day

What is the difference between Python's list methods append and extend?

append: Appends object at the end.

x = [1, 2, 3]
x.append([4, 5])
print (x)

Output:

[1, 2, 3, [4, 5]]

extend: Extends list by appending elements from the iterable.

x = [1, 2, 3]
x.extend([4, 5])
print (x)

Output:

[1, 2, 3, 4, 5]

Ref: https://bit.ly/2AZ6ZFq