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There are **30** NRICH Mathematical resources connected to **Geometric sequences**, you may find related items under Patterns, sequences and structure.

Problem
Primary curriculum
Secondary curriculum
### Summing Geometric Progressions

Watch the video to see how to sum the sequence. Can you adapt the method to sum other sequences?

Age 14 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Tower of Hanoi

The Tower of Hanoi is an ancient mathematical challenge. Working on the building blocks may help you to explain the patterns you notice.

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Clickety Click and All the Sixes

What is the sum of: 6 + 66 + 666 + 6666 ............+ 666666666...6 where there are n sixes in the last term?

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Sixty-seven Squared

Evaluate these powers of 67. What do you notice? Can you convince someone what the answer would be to (a million sixes followed by a 7) squared?

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Tiny Nines

What do you notice about these families of recurring decimals?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### The Tomato and the Bean

At the beginning of May Tom put his tomato plant outside. On the same day he sowed a bean in another pot. When will the two be the same height?

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Circles Ad Infinitum

A circle is inscribed in an equilateral triangle. Smaller circles touch it and the sides of the triangle, the process continuing indefinitely. What is the sum of the areas of all the circles?

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Converging Product

In the limit you get the sum of an infinite geometric series. What about an infinite product (1+x)(1+x^2)(1+x^4)... ?

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### The Amazing Splitting Plant

Can you work out how many flowers there will be on the Amazing Splitting Plant after it has been growing for six weeks?

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Magic Plant

On Friday the magic plant was only 2 centimetres tall. Every day it doubled its height. How tall was it on Monday?

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Vanishing Point

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

Age 14 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Clickety Click

What is the sum of: 6 + 66 + 666 + 6666 ............+ 666666666...6 where there are n sixes in the last term?

Age 16 to 18

ShortChallenge Level

Problem
Primary curriculum
Secondary curriculum
### Geometric Parabola

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

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Mobile Numbers

In this investigation, you are challenged to make mobile phone numbers which are easy to remember. What happens if you make a sequence adding 2 each time?

Age 5 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Production Equation

Each week a company produces X units and sells p per cent of its stock. How should the company plan its warehouse space?

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Investigating Pascal's Triangle

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

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Von Koch Curve

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.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Sierpinski Triangle

What is the total area of the triangles remaining in the nth stage of constructing a Sierpinski Triangle? Work out the dimension of this fractal.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Golden Fibs

When is a Fibonacci sequence also a geometric sequence? When the ratio of successive terms is the golden ratio!

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Generally Geometric

Generalise the sum of a GP by using derivatives to make the coefficients into powers of the natural numbers.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Smaller and Smaller

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?

Age 7 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Ruler

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?

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Transformations Tables

These grids are filled according to some rules - can you complete them?

Age 7 to 11

Challenge Level

Interactive
Primary curriculum
Secondary curriculum
### Proof Sorter - Geometric Sequence

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

Age 16 to 18

Challenge Level

Article
Primary curriculum
Secondary curriculum
### 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.

Age 16 to 18

Problem
Primary curriculum
Secondary curriculum
### Squaring the Circle and Circling the Square

If you continue the pattern, can you predict what each of the following areas will be? Try to explain your prediction.

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Binary Squares

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

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### The Great Tiling Count

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

Age 7 to 11

Challenge Level