Education Technology

Tetrahedral Numbers

Activity Overview

This activity extends upon the triangular numbers. The tetrahedral numbers are inclusive of the triangular numbers, can also be found in Pascal's triangle, can be represented visually and provide a wealth of opportunities through inductive proof.


Students use inductive proof to verify the rule they establish for the tetrahedral numbers and also the sum of whole numbers squared.


  • Induction
  • Proof
  • Tetrahedral numbers
  • Triangular numbers
  • Summation

About the Lesson

In this activity students explore the tetrahedral numbers and develop formulas from diagrams, Pascal's triangle and prior knowledge (Triangular Numbers). Once students have established a reliable formula they use inductive proof to show that the formula works for all values of n. Additional inductive proofs are included on related patterns including the sum of whole numbers squared.