Sequences summary

Key learning points

• Common difference $d$ → $n$th term $a+(n-1)d$ or $dn+c$.
• Quadratic sequences: second differences constant.
• Always test your $n$th term on the first two given terms.

Worked example 1 — Linear nth term

Sequence $5,8,11,14,\ldots$. $n$th term?

Working

Common difference 3.

Worked example 2 — Next term

$2,6,12,20,\ldots$ next term?

Working

Second differences constant.

Worked example 3 — Membership

Is $50$ in $4n+2$?

Working

Solve for positive integer $n$.

Scaffolded Learning Sheet and answers (PDFs)

This page is a short, searchable overview for revision and search engines. Use the Scaffolded Learning Sheet first, then the Answers PDF for a full written solution. The printable PDFs remain the main classroom resource.