Geometric sequences

  • Converging Product
    problem
    Favourite

    Converging Product

    Age
    16 to 18
    Challenge level

    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)... ?

  • Circles ad infinitum
    problem
    Favourite

    Circles Ad Infinitum

    Age
    16 to 18
    Challenge level

    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?

  • content-03-01-cupboardlove2-sol1.gif
    problem

    Transformations Tables

    Age
    7 to 11
    Challenge level
    These grids are filled according to some rules - can you complete them?
  • Clickety Click
    problem

    Clickety Click

    Age
    16 to 18
    Challenge level
    What is the sum of: 6 + 66 + 666 + 6666 ............+ 666666666...6 where there are n sixes in the last term?
  • Golden Fibs
    problem

    Golden Fibs

    Age
    16 to 18
    Challenge level
    When is a Fibonacci sequence also a geometric sequence? When the ratio of successive terms is the golden ratio!
  • Sierpinski Triangle
    problem

    Sierpinski Triangle

    Age
    16 to 18
    Challenge level
    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.
  • Production Equation
    problem

    Production Equation

    Age
    16 to 18
    Challenge level
    Each week a company produces X units and sells p per cent of its stock. How should the company plan its warehouse space?
  • Smaller and Smaller
    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?
  • Mobile Numbers
    problem

    Mobile Numbers

    Age
    5 to 11
    Challenge level

    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?

  • The Great Tiling Count
    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.

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