IB Maths: Arithmetic Sequences & Series FAQ

An arithmetic sequence has a constant common difference $d$ between consecutive terms; an arithmetic series is the sum of those terms. It's examined in Paper 1 (no calculator) as short-answer questions using $u_n=u_1+(n-1)d$ and $S_n=\frac{n}{2}(2u_1+(n-1)d)$, and occasionally inside longer Paper 2 problem-solving questions.

A sequence is a list of terms — 3, 7, 11, 15 — each one generated by adding a fixed common difference. A series is what you get when you add those terms together: 3+7+11+15 = 36. IB questions test both separately, so read carefully whether you're asked for a term or a sum.

You need the general term $u_n=u_1+(n-1)d$ and the sum formula $S_n=\frac{n}{2}(2u_1+(n-1)d)$, which can also be written $S_n=\frac{n}{2}(u_1+u_n)$. Both are printed in the IB formula booklet, so memorising them isn't the challenge — knowing which one to reach for is.

Yes. Both the $n$th term formula and the sum-to-$n$-terms formula appear in the IB Mathematics formula booklet under the Topic 1 (Number & Algebra) section, identical for AA and AI, SL and HL. You don't need to derive them from scratch in an exam unless a question specifically asks you to prove a result.

Check that the difference between every pair of consecutive terms is the same constant $d$. If term two minus term one equals term three minus term two, and that pattern holds throughout, it's arithmetic. If the ratio (not difference) is constant instead, you're looking at a geometric sequence — a different topic entirely.

The three I see most often in fifteen years of marking: mixing up $u_n$ (a term) with $S_n$ (a sum), forgetting that $n$ must be a positive integer when solving for it, and misreading whether the first term given is $u_1$ or $u_0$. Each one costs an easy method mark that's otherwise straightforward.

They connect directly to geometric sequences (Topic 1.3), financial applications like loan repayments in Applications and Interpretation, and sigma notation $\sum$, which the IB introduces alongside series work. HL students also meet arithmetic sequences again inside proof by induction questions.

They appear most years, usually as one short-answer question worth 4-7 marks on Paper 1, sometimes embedded in a longer Paper 2 context question worth more. It's rarely a whole exam question on its own at HL, but it's a reliable, learnable source of marks if you know the two core formulas cold.

Arithmetic sequences add a constant difference $d$ between terms; geometric sequences multiply by a constant ratio $r$. Their sum formulas look different too — arithmetic sums grow linearly with $n$, while geometric sums can converge to a finite value if $|r|<1$, which arithmetic series never do.

The core formulas are identical in both subjects — the IB doesn't change the maths. What differs is context and depth: Applications and Interpretation leans on real-world financial and modelling scenarios, while Analysis and Approaches is more likely to test pure algebraic manipulation or link it to proof at HL.

Not really — the formulas and question style are almost identical at SL and HL. The real difference at HL is that this topic feeds into proof by mathematical induction, which is HL-only content, so HL students need a firmer grip on the underlying logic, not just the arithmetic.

Work through past-paper style questions under timed conditions, not just textbook drill exercises — the IB tests this topic through worded contexts more than raw formula substitution. On RevisionPrep, Topical Worksheets group these questions by difficulty so you can build from basic term-finding up to multi-step series problems.

Yes — alongside free past papers on the IB's own resource platforms, RevisionPrep offers Revision Notes covering the formulas and worked logic, Topical Worksheets for repeated practice, and full Mock Papers so your child can see how this topic sits inside a real timed exam.