Geometric sequences

problem

Smaller and Smaller

Age

7 to 14

Challenge level

Can you predict, without drawing, what the perimeter of the next shape in this pattern will be if we continue drawing them in the same way?
problem

The Great Tiling Count

Age

7 to 11

Challenge level

Compare the numbers of particular tiles in one or all of these three designs, inspired by the floor tiles of a church in Cambridge.
problem

Investigating Pascal's Triangle

Age

7 to 11

Challenge level

In this investigation, we look at Pascal's Triangle in a slightly different way - rotated and with the top line of ones taken off.
problem

Geometric Parabola

Age

14 to 16

Challenge level

Explore what happens when you draw graphs of quadratic equations with coefficients based on a geometric sequence.
problem

Vanishing Point

Age

14 to 18

Challenge level

How can visual patterns be used to prove sums of series?
problem

Ruler

Age

16 to 18

Challenge level

The interval 0 - 1 is marked into halves, quarters, eighths ... etc. Vertical lines are drawn at these points, heights depending on positions. What happens as this process goes on indefinitely?
problem

Binary Squares

Age

16 to 18

Challenge level

If a number N is expressed in binary by using only 'ones,' what can you say about its square (in binary)?
problem

Von Koch Curve

Age

16 to 18

Challenge level

Make a poster using equilateral triangles with sides 27, 9, 3 and 1 units assembled as stage 3 of the Von Koch fractal. Investigate areas & lengths when you repeat a process infinitely often.
article
Sum the Series

This article by Alex Goodwin, age 18 of Madras College, St Andrews describes how to find the sum of 1 + 22 + 333 + 4444 + ... to n terms.
interactivity
Proof Sorter - Geometric Sequence

Age

16 to 18

Challenge level

Can you correctly order the steps in the proof of the formula for the sum of the first n terms in a geometric sequence?