Learning pack · Foundation · CIE Core

Sequences

What's in this pack: printable worksheet PDF, matching answers PDF (Foundation · CIE Core depth). Sequences follow rules: term-to-term or position-to-term ( $n$ th term). Linear sequences have a constant difference.

Resources at the top · full summary · videos with short notes below.

🎒 Resources in this pack

Jump straight to the printable files, or scroll to the summary and videos.

Scaffolded Learning Sheet — attempt the worksheet, then use the Answers for a full written solution.

📝 Open Learning Sheet ✅ Open answers 🎬 More topic videos (6)📖 Full summary

Files: foundation-16 Sequences handout.pdf · foundation-16 Sequences handout answers.pdf

Full topic summary

Sequences follow rules: term-to-term or position-to-term ( $n$ th term). Linear sequences have a constant difference.

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

3n+2

Common difference 3.

Worked example 2 — Next term

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

Working

30

Second differences constant.

Worked example 3 — Membership

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

Working

n=12\Rightarrow\text{yes}

Solve for positive integer $n$ .

🎬 Topic videos

Fibonacci Numbers hidden in the Mandelbrot Set - Numberphile
Numberphile · 10 min
Enrichment / curiosity clip for Lower Secondary (Numberphile-style). Use for hooks, clubs, or stretch — not core exam content.
Random Fibonacci Numbers - Numberphile
Numberphile · 11 min
Enrichment / curiosity clip for Lower Secondary (Numberphile-style). Use for hooks, clubs, or stretch — not core exam content.
A Sequence with a Mistake - Numberphile
Numberphile · 3 min
Enrichment / curiosity clip for Lower Secondary (Numberphile-style). Use for hooks, clubs, or stretch — not core exam content.
The fabulous Fibonacci flower formula
Mathologer · 11 min
Enrichment / curiosity clip for Lower Secondary (Numberphile-style). Use for hooks, clubs, or stretch — not core exam content.
How did Fibonacci beat the Solitaire army?
Mathologer · 23 min
Enrichment / curiosity clip for Lower Secondary (Numberphile-style). Use for hooks, clubs, or stretch — not core exam content.
The nth Term - Corbettmaths
Corbettmaths · 6 min
Lower Secondary classroom-friendly explainer. Scaffold→stretch friendly; use with mixed-ability groups.

More Lower Secondary packs

Browse the hub Learning Packs & Summary, or open the compact Sequences summary.