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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
A pattern has rule T(n)=an2+b, where a and b are constant. Stages 1,2 and 3 contain 3,9 and 19 tiles. How many tiles are at stage 10?
Show worked answer
Answer: 201
- The second difference is 4
- a=2.
- Stage 1 gives b=1.
- Then T(10)=2×102+1=201.
Example 2
Stage n contains n2+6n+4 tiles. Which positive whole-number stage contains 76 tiles?
Show worked answer
Answer: 6
- Rearrange to n2+6n−72=0=(n−6)(n+12).
- The positive stage is 6.
Example 3
A pattern has rule T(n)=an2+b, where a and b are constant. Stages 1,2 and 3 contain 7,25 and 55 tiles. How many tiles are at stage 8?
Show worked answer
Answer: 385
- The second difference is 12
- a=6.
- Stage 1 gives b=1.
- Then T(8)=6×82+1=385.
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