Arithmetic sequences

  • Maxagon
    problem

    Maxagon

    Age
    11 to 14
    Challenge level
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    What's the greatest number of sides a polygon on a dotty grid could have?

  • What numbers can we make now?
    problem

    What numbers can we make now?

    Age
    11 to 14
    Challenge level
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    Imagine we have four bags containing numbers from a sequence. What numbers can we make now?

  • Charlie's delightful machine
    problem

    Charlie's delightful machine

    Age
    11 to 16
    Challenge level
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    Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?

  • A little light thinking
    problem

    A little light thinking

    Age
    14 to 16
    Challenge level
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    Here is a machine with four coloured lights. Can you make two lights switch on at once? Three lights? All four lights?

  • Steel Cables
    problem

    Steel cables

    Age
    14 to 16
    Challenge level
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    Some students have been working out the number of strands needed for different sizes of cable. Can you make sense of their solutions?

  • Mystic Rose
    problem

    Mystic rose

    Age
    14 to 16
    Challenge level
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    Use the animation to help you work out how many lines are needed to draw mystic roses of different sizes.

  • Prime AP
    problem

    Prime AP

    Age
    16 to 18
    Challenge level
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    What can you say about the common difference of an AP where every term is prime?

  • Prime sequences
    problem

    Prime sequences

    Age
    16 to 18
    Challenge level
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    This group tasks allows you to search for arithmetic progressions in the prime numbers. How many of the challenges will you discover for yourself?
  • Speedy summations
    problem

    Speedy summations

    Age
    16 to 18
    Challenge level
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    Watch the video to see how to add together an arithmetic sequence of numbers efficiently.

  • Polite Numbers
    problem

    Polite numbers

    Age
    16 to 18
    Challenge level
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    A polite number can be written as the sum of two or more consecutive positive integers, for example 8+9+10=27 is a polite number. Can you find some more polite, and impolite, numbers?