Is Topic 2 (Sequences and Series) in Paper 1 or Paper 2?

Topic 2 is Pure Mathematics and can appear in Paper 1 (100 marks) or Paper 2 Section A (40 marks). Expect financial modelling questions that combine AP/GP with real-world contexts.

Can I use the GC to find terms and partial sums?

Yes. The GC SEQ or RECUR mode is useful for checking your analytic answers. However, you must still show the formula and working - simply quoting a calculator output without method steps will not earn full marks.

Do I need to memorise the standard sum formulas, or are they given?

The AP and GP sum formulas are not provided in the SEAB formula list, so they must be memorised. Standard sigma identities (\$\sum k\$, \$\sum k^2\$) are also not on the reference sheet. ---

H2 Maths Sequences and Series | Free Notes

Study guide07 Oct 2025, 00:00 Z

H2 Maths sequences and series notes: key formulas for AP/GP, worked examples, sigma notation, and exam techniques for convergence questions.

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Q: What does H2 Maths Notes (JC 1-2): 2) Sequences and Series cover?
A: Arithmetic and geometric progressions, convergence tests, sigma notation, and calculator workflows for modelling recurrence relations.

Before you start
Refresh IP-level arithmetic and geometric sequences. Revisit the MOE definitions so your notation matches the mark scheme and set your graphing calculator (GC) to Exam Mode before drilling.

Terms and sums are different objects: Label $u_n$ and $S_n$ .
Recurrence questions need the next-term rule: Generate a few terms before generalising.
Modelling questions need interpretation: State what the limit, sum, or divergence means in context.

Concrete example: In a savings recurrence, $u_{n+1}=1.005u_n+200$

Reviewed by

Marcus Pang·Managing Director (Maths)

Wording clue	Quantity wanted	First setup	Common trap
"Find the 20th term"	One term, $u_{20}$	Use the AP or GP term formula.	Using $S_n$ because the word "series" appears nearby.
"Total after 20 deposits"	Partial sum, $S_{20}$	Decide whether the first deposit grows for 19 or 20 periods.	Off-by-one errors in finance recurrences.
"Long-run total" or "sum to infinity"	Infinite sum, $S_\infty$	Check $\lvert r\rvert \lt 1$ before substituting.	Applying $S_\infty$
"Given $u_{n+1}$ in terms of $u_n$ "	Recurrence output or limiting behaviour	Generate terms, then solve the recurrence if needed.	Treating a recurrence like an explicit formula immediately.

H2 Maths Sequences and Series | Free Notes

2.1 | Language and Notation

Core ideas

Arithmetic progressions (AP)

Geometric progressions (GP)

Term-or-sum checkpoint

2.2 | Worked Examples

2.3 | Calculator Workflows

2.4 | Exam Watch Points

Practice Quiz

2.5 | Quick Revision Checklist

Common exam mistakes

Frequently asked questions

Sources

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