Geometric sequences

  • Magic Plant
    problem
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    Magic Plant

    Age
    5 to 7
    Challenge level
    filled star filled star empty star

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

  • problem
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    The Amazing Splitting Plant

    Age
    5 to 7
    Challenge level
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    Can you work out how many flowers there will be on the Amazing Splitting Plant after it has been growing for six weeks?

  • The tomato and the bean
    problem
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    The Tomato and the Bean

    Age
    5 to 7
    Challenge level
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    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?

  • Pocket money
    problem
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    Pocket Money

    Age
    11 to 14
    Challenge level
    filled star empty star empty star

    Which of these pocket money systems would you rather have?

  • The Tower of Hanoi - three wooden poles, with several coloured rings of decreasing sizes on the middle pole.
    problem
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    Tower of Hanoi

    Age
    11 to 14
    Challenge level
    filled star filled star empty star

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

  • Double Trouble
    problem
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    Double Trouble

    Age
    14 to 16
    Challenge level
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    Simple additions can lead to intriguing results...

  • Tiny Nines
    problem
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    Tiny Nines

    Age
    14 to 16
    Challenge level
    filled star filled star empty star

    What do you notice about these families of recurring decimals?

  • Summing geometric progressions
    problem
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    Summing Geometric Progressions

    Age
    14 to 18
    Challenge level
    filled star empty star empty star

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

  • Sixty-Seven Squared
    problem
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    Sixty-Seven Squared

    Age
    16 to 18
    Challenge level
    filled star empty star empty star
    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?
  • Clickety Click and all the Sixes
    problem
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    Clickety Click and All the Sixes

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