Sequences and series are usually the first topic students meet in IB DP maths, and they set the tone for the course. They are also one of the most practical: the same formulas run savings accounts, car depreciation and home loans. Get them secure early and you collect easy marks on every paper.
What all students cover (AA and AI, SL)
- Arithmetic sequences and series: uₙ = u₁ + (n − 1)d, and the sum Sₙ.
- Geometric sequences and series: uₙ = u₁rⁿ⁻¹, and the sum Sₙ.
- Sigma notation.
- Applications: growth and decay, simple patterns in real contexts.
- Financial applications of geometric sequences: compound interest and annual depreciation.
AA SL also includes the sum to infinity of a geometric series (when |r| < 1). AI SL goes further into finance: loans, amortisation and annuities, using the GDC's financial solver.
Note for future students: in the new course (first exams May 2029), financial applications leave AA. Students sitting exams in 2027 and 2028 still need them.
The traps that cost marks
- n or n − 1? The nth term uses (n − 1); students often use n. Check with u₁.
- "After 5 years" vs "in the 5th year". Read carefully – it changes n.
- Sum to infinity without checking |r| < 1. If a question asks you to justify, say why it converges.
- Rounding money too early. Keep full accuracy until the final answer, then give money to 2 decimal places (or as the question says).
- Depreciation is a decrease: r = 1 − rate, not 1 + rate.
The GDC financial solver (TVM): getting it right
The time-value-of-money solver has five main inputs. Most errors are in setting them up, not in the maths:
- N – number of payment periods (years × periods per year).
- I% – the annual interest rate as a percentage.
- PV – present value; PMT – regular payment; FV – future value.
- P/Y and C/Y – payments per year and compounding periods per year.
Two rules prevent most mistakes:
- Money paid out is negative, money received is positive. If you deposit ₹1,00,000, PV is −100000.
- Match P/Y and C/Y to the question. "Compounded monthly" with annual payments needs C/Y = 12, P/Y = 1.
And always write the inputs in your answer – for example "N = 10, I% = 6, PV = −5000, P/Y = C/Y = 12 → FV = …". The markscheme gives method marks for the setup; a bare number earns little if it is wrong.
How this topic connects to the rest of the course
- Geometric series lead to exponential functions and, in AA HL, to Maclaurin series.
- Sigma notation appears again in statistics and proof by induction (HL).
- Financial maths is a popular internal assessment area for AI students.
A short practice plan
- Week 1: arithmetic and geometric formulas by hand, with plenty of "find n" questions.
- Week 2: financial questions, first by formula, then with the TVM solver.
- Week 3: past-paper questions mixed with other topics, marked against the markscheme.
How Maths Bodhi helps
Sequences are often where a new DP student decides whether IB maths is "for them". We use this topic to build confidence early:
- A diagnostic of algebra and indices – the foundations under every sequence question.
- Context reading drills ("in the 5th year" vs "after 5 years").
- TVM solver practice on the student's own calculator, with the written setup the markscheme expects.
- Past IB questions marked against the markscheme, with a short note on what to fix.
Ajay Vatsyayan (M.Tech, 14+ years teaching maths) teaches IB DP maths at Maths Bodhi and has taught students from schools across Gurgaon, including Scottish High International School, Shiv Nadar School, Amity Global School and Lancers International School. Maths Bodhi is independent and not affiliated with any school. Read Ajay's profile, or see our IB algebra tutor, AA SL and AI SL pages.
Home sessions across Gurgaon – including Golf Course Road – or online. For students just starting the DP, read our summer plan before IB DP maths. Book a free demo class.
Related: GDC skills for IB maths, how to get a 7 in IB maths and the IB DP maths guide for Gurgaon families.
Course content checked against the current IB AA and AI guides and the 2029 update notes by the Maths Bodhi team (October 2026). Teaching plan reviewed by Ajay Vatsyayan.
Frequently asked questions
- Is financial maths in IB maths AA?
- Yes, for exams in 2027 and 2028: AA SL includes compound interest and depreciation as applications of geometric sequences. Financial applications leave AA in the new course with first exams in May 2029. AI SL covers finance in more depth, including loans and annuities.
- What is the most common mistake with the TVM solver?
- Getting the sign convention or compounding settings wrong. Money paid out is negative, and P/Y and C/Y must match the question.
- When can I use the sum to infinity of a geometric series?
- Only when the common ratio satisfies |r| < 1, so the series converges.