Quadratic Number Patterns

Quadratic Number Patterns

A quadratic number pattern has constant second differences. First differences change, but the differences between those changes stay fixed. Build a table with term number, value, first difference and second difference. This is more reliable than trying to guess a formula from the first few terms.

Worked reasoning

For $3,8,15,24,35$, first differences are 5,7,9,11; second differences are 2,2,2. The constant second difference identifies a quadratic pattern.

Exam method

1. List terms in order. 2. Calculate first then second differences. 3. Use the constant second difference as evidence for a quadratic rule.

Read a differences table as evidence

A differences table is not busywork. It distinguishes a linear sequence, a quadratic sequence and a sequence that needs another model. Put term positions in a separate column so a missing term can be found without confusing its value with its place. In an exam explanation, write ‘the second differences are constant’ rather than only giving the next term. This supplies evidence for the quadratic conclusion and makes your reasoning reproducible.

One-minute retrieval: Quadratic Number Patterns

Close the worked solution. From memory, state its central rule, name one condition that makes it valid, and reconstruct one check that would catch a typical exam error.