Arithmetic sequences

There are 49 NRICH Mathematical resources connected to Arithmetic sequences
What numbers can we make now?
problem
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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?

Growing Surprises
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Growing surprises

Age
11 to 14
Challenge level
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Can you find the connections between linear and quadratic patterns?
Steel Cables
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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?
Odds, Evens and More Evens
problem
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Odds, evens and more evens

Age
11 to 14
Challenge level
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Alison, Bernard and Charlie have been exploring sequences of odd and even numbers, which raise some intriguing questions...

Missing Middles
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Missing middles

Age
5 to 7
Challenge level
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Can you work out the domino pieces which would go in the middle in each case to complete the pattern of these eight sets of three dominoes?
Seven Squares - Group-worthy Task
problem
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Seven squares - group-worthy task

Age
11 to 14
Challenge level
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Choose a couple of the sequences. Try to picture how to make the next, and the next, and the next... Can you describe your reasoning?
Seven Squares
problem
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Seven squares

Age
11 to 14
Challenge level
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Watch these videos to see how Phoebe, Alice and Luke chose to draw 7 squares. How would they draw 100?
Domino Sequences
problem
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Domino sequences

Age
5 to 7
Challenge level
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Find the next two dominoes in these sequences.
Coordinate Patterns
problem
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Coordinate patterns

Age
11 to 14
Challenge level
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Charlie and Alison have been drawing patterns on coordinate grids. Can you picture where the patterns lead?
Squares in rectangles
problem
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Squares in rectangles

Age
11 to 14
Challenge level
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A 2 by 3 rectangle contains 8 squares and a 3 by 4 rectangle contains 20 squares. What size rectangle(s) contain(s) exactly 100 squares? Can you find them all?