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Number Sequences: what comes next?

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Ten patterns, one missing number each. Work out the rule and type the next term. Use the Gaps hint to see the differences, and read the explanation of every rule afterwards.

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How to play Number Sequences

  1. Choose a level from simple adding up to mixed expert patterns.
  2. Look at the numbers and find the rule that connects them.
  3. Type the next number and press Enter or Check. You get two tries.
  4. Press Gaps if you want a clue: it shows the difference between each pair of neighbours.
  5. After every pattern you see the rule explained, so you learn it even when you get it wrong.

Tips and strategy

  • Always check the differences first. If they are all the same, you have an adding or subtracting pattern.
  • If the differences grow steadily (+2, +3, +4), you have triangular numbers. If they double, look for powers of 2.
  • If each number is the same multiple of the one before it, multiply by that number.
  • Numbers that grow fast but not by a fixed ratio might be squares (1, 4, 9, 16) or cubes (1, 8, 27, 64).
  • If the pattern looks odd, try looking at every second number.

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FAQ

Number Sequences: questions

What is a number sequence?

A list of numbers that follows a rule. Finding the rule lets you predict any term, which is the first step towards algebra.

What is the Fibonacci sequence?

A sequence where each number is the sum of the two before it, like 1, 1, 2, 3, 5, 8, 13. It appears in nature, from sunflower seeds to shells.

What are triangular numbers?

Numbers that can be arranged in a triangle of dots: 1, 3, 6, 10, 15. The gaps between them grow by 1 each time (+2, +3, +4, +5).

Are the answers always whole numbers?

Yes, every pattern in this game uses whole numbers, so you only type digits.

What ages is it for?

Roughly 8 and up. Level 1 suits Year 3 or 4 and Level 5 is a real challenge for secondary students and adults.

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