Infer a quadratic pattern and use it to find or compare stages.
Free examples and worked answers. No account needed.
Practise the method.
Infer a quadratic pattern and use it to find or compare stages.
Infer a quadratic pattern and use it to find or compare stages.
Example 1
An arithmetic pattern adds the same number at every stage. Stage 4 has 26 tiles and stage 6 has 38. How many tiles are at stage 9?
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Answer: 56
Across 2 stages, the increase is 12
each stage adds 6.
From stage 4, add 5×6:56 tiles.
Example 2
Pattern A adds a constant number each stage: stage 2 has 20 tiles and stage 4 has 34. Pattern B has n+90 tiles at stage n. At which positive stage are the counts equal?
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Answer: 14
Pattern A adds 7 each stage
A(n)=7n+6.
Equate it to n+90 and solve the linear equation: n=14.
Example 3
An arithmetic pattern adds the same number at every stage. Stage 5 has 23 tiles and stage 7 has 29. How many tiles are at stage 11?
Show worked answer
Answer: 41
Across 2 stages, the increase is 6
each stage adds 3.
From stage 5, add 6×3:41 tiles.
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