GCSE Maths: Sequences: patterns

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1. What is the first step in finding a pattern rule for a sequence of shapes?

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   Look at how the pattern changes from one step to the next—identify whether elements are being added, multiplied, or following another operation.

2. In a linear sequence pattern, what does the constant difference between consecutive terms tell you?

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   It tells you the coefficient (multiplier) of n in the algebraic expression for the pattern.

3. Why might a specific number of elements be impossible to make in a pattern sequence?

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   Because the pattern only generates certain values (e.g., only odd numbers, or only multiples of 3), so numbers outside that set cannot be formed.

4. To find which pattern number produces exactly k elements, what equation should you solve?

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   Set your pattern expression equal to k and solve for n. For example, if the pattern is 3n + 1, solve 3n + 1 = k.

5. When a pattern uses two different shapes (e.g., squares and triangles), how should you analyse it?

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   Find separate expressions for each shape type in terms of n, then combine them if needed for the total.

6. How can you find the number of elements in pattern 801 if you know pattern 800 has 2401 elements?

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   Add the constant difference (the amount added each step). Identify the pattern rule and add the increment once.

7. What does it mean to write an expression 'in terms of n' for a pattern?

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   To write an algebraic formula using n (the pattern number) that calculates the number of elements in any pattern.