Number Sequences

Learning Objectives


In this challenge we are going to apply our programming skills to perform some arithmetic operations. We will use arithmetic operators such as +, – and * as well as for loops to repeat instructions.

Context / Starter activity


A primary teacher likes to start her maths lesson by displaying a number sequence maths challenge on the board. Here are the last three challenges she has used with her class. Can you solve these?

Number Sequence #1:number-sequence-2
Number Sequence #2:number-sequence-3
Number Sequence #3:number-sequence-1

Number Sequences


There are different types of number sequences. Let’s investigate the most widely used types of number sequences.
You may want to read this page first: https://www.mathsisfun.com/numberpatterns.html

Arithmetic Sequences

An Arithmetic Sequence is made by adding the same value each time. When creating an arithmetic number sequence you have to decide of a starting number (e.g. “2”) and an increment (e.g. “3”)

number-sequence-diagram-1

Geometric Sequences

A Geometric Sequence is made by multiplying by the same value each time.
When creating a geometric number sequence you have to decide of a starting number (e.g. “2”) and a multiplier (e.g. “3”)

number-sequence-diagram-2

Square Numbers

1,4,9,16,25,36…

This sequence consists of calculating the squares of whole numbers.

number-sequence-diagram-3

Incremental Sequence

1, 2, 4, 7, 11, 16, 22, 29, 37, …

This sequence is generated by adding an “increasing” number, that is a number that each time is incremented by 1 as we progress through the number sequence. Not clear? Check the diagram below.

number-sequence-diagram-4

Fibonacci Numbers

1, 2, 3, 5, 8, 13, 21, 34, …

The Fibonacci Sequence is found by adding the two numbers before it together.

  • The 3 is found by adding the two numbers before it (1+2)
  • The 5 is found by adding the two numbers before it (2+3)
  • The 8 is found by adding the two numbers before it (3+5)

number-sequence-diagram-5

Python Code


Arithmetic Sequence


Triangular Numbers


Fibonacci Numbers

Challenge #1


Edit some of the above scripts to create other number sequences such as:

  • Arithmetic sequences using a different starting number and increment,
  • Geometric sequences,
  • Square numbers sequence.

You can also adapt or even mix these techniques to create your own number sequences!

Challenge #2


Adapt your scripts so that the program asks the end-user the question: “What number comes next in the sequence?” The user has to type their answer. The program should check if they have got the right answer or not.

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