Education Technology

The Fibonacci Sequence

Published on 01/07/2018

Activity Overview

One of the simplest and beautiful mathematical sequences. The simplicity: 1, 1, 2, 3, 5, 8 ... is such that each term is the sum of the previous two terms. Examples of the sequence can be found in nature, architecture and number theory. In this investigation, students explore some of the patterns within the sequence such as the consecutive sum of the squared terms. What about the last digit of term 60, 61, 62 ... what pattern do these form? Don't worry, the magical phi is not left out, including amazing relationships such as 1 + phi. Check it out!


  • Investigate limits in sequences
  • Generate sequences beyond Arithmetic and Geometric
  • Develop techniques for exploring sequences using technology.


  • Sequence
  • Sum
  • Ratio

About the Lesson

What is the ratio between consecutive terms in the Fibonacci sequence? What special properties does this value have? Try squaring this number to see what you get. Try cubing the number. What about adding up consecutive squared terms? This activity puts together a feast of relationships not often explored in the Fibonacci sequence. There are lots more you could do, this activity explores just a collection from this amazing sequence.