M11 Sequences mind map

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M11 Sequences mind map

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Rules

Kinds: Term-to-term finds next; position-to-term uses n
Recognise: Squares, cubes, triangular; Fibonacci adds previous two

Linear

Difference: 5,8,11,… → 3n+2; decreasing → negative coefficient
Membership: Solve nth term = value; n must be positive integer
Patterns: Sticks: 3n+1; few values alone do not fix one rule

Quadratic

Second difference: Constant non-zero second difference → quadratic
Coefficient: Higher: Second difference = 2a; subtract an² then find linear part

Geometric

Ratio: Multiply by same ratio; may grow or decay
Nth term: Higher: ar^(n−1); 5×3^(n−1) gives fifth term 405

Connections

Rules → Quadratic: Second differences identify a quadratic position rule
Rules → Geometric: Multiplication by a fixed ratio gives geometric terms