A curious sequence

Last updated: 15/11/2023
Contributor: David Benjamin 🐝
A curious sequence
Main Subject
Key stage
Category
Algebra: Sequences worksheets
Inside
Includes answers
Resource type
Student activity
Maths
Reasoning
Maths
Problem solving

This nifty investigation ties together your work on sequences with decimal-fraction equivalence and Pythagorean triples. It also introduces the idea of limits.

Starting with a sequence of fractions, students need to

  • identify how to create each term from the previous
  • use a calculator to convert to decimals and discover the limit of the sequence is √2
  • split the numerators of the fractions into two consecutive numbers, forming Pythagorean triples within each odd term
  • discover the result of changing the first term.

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