MYP Maths: Arithmetic & Geometric Patterns FAQ

Students usually spot the pattern fine — the trouble is turning it into a formal rule using algebraic notation and then proving it works for a term they weren't given. That justification step, not the spotting, is where most marks get lost in Criterion B: Investigating Patterns.

An arithmetic sequence adds (or subtracts) the same fixed number — the common difference, d — to get each next term, like 3, 7, 11, 15. A geometric sequence multiplies by a fixed common ratio, r, instead, like 3, 6, 12, 24. Same underlying idea, completely different growth pattern.

Use the formula u_n = u_1 + (n − 1)d, where u_1 is the first term and d is the common difference between consecutive terms. For the sequence 5, 8, 11, 14…, d = 3 and u_1 = 5, so the 10th term is u_10 = 5 + 9(3) = 32.

Use u_n = u_1 × r^(n−1), where r is the common ratio found by dividing any term by the one before it. For 3, 6, 12, 24…, r = 2, so the 7th term is u_7 = 3 × 2^6 = 192 — a value you'd never reach by simply extending the list by hand.

A sequence is just the ordered list of terms — 2, 5, 8, 11. A series is what you get when you add those terms together: 2 + 5 + 8 + 11 = 26. Students regularly lose marks by giving a sequence when a question actually asks for a sum.

Pattern work is examined under MYP Criterion B: Investigating Patterns, one of four criteria (A, B, C, D) that each carry a maximum of 8 achievement levels. According to the IB's MYP: Mathematics guide, Criterion B specifically rewards students who select a technique, describe a general rule, then justify or prove it.

Top marks (achievement levels 7–8) need three things: a rule written in correct algebraic notation (like u_n = 2n + 1), a test of that rule against a term you weren't given, and a written or algebraic justification for why it always works. Skip the justification and most answers cap at level 5–6.

The biggest one: forgetting that a negative common ratio makes terms alternate in sign, so predictions for later terms come out wrong. Others confuse u_n (the term's value) with n (its position), or write u_1 × r^n instead of u_1 × r^(n−1), which shifts every single answer by one term.

Check consecutive differences first — if they're constant, it's arithmetic. If not, check consecutive ratios instead — constant ratios mean geometric. If neither is constant, look at second differences: a constant second difference usually signals a quadratic pattern rather than a linear or exponential one.

Yes. Number patterns sit within the Number and Algebra strand of the MYP on-screen eAssessment, typically sat in MYP Year 5, and questions often ask students to generalise a pattern algebraically rather than just extend a list of numbers. Investigating Patterns-style tasks, mirroring Criterion B, show up regularly.

Arithmetic and geometric sequences and series form part of Topic 1 (Number and Algebra) in both DP Mathematics: Analysis and Approaches and Applications and Interpretation, first examined in 2021. The nth-term skills built in MYP 4-5 become the sigma-notation and compound-interest problems you'll meet at DP level.

You need the nth-term formula for arithmetic sequences (u_n = u_1 + (n−1)d) and for geometric sequences (u_n = u_1 × r^(n−1)). Extended Mathematics classes also introduce the sum formulas for both sequence types, laying groundwork for sigma notation you'll meet later in the DP.

Yes — both cover arithmetic and geometric patterns, but Extended Mathematics pushes further into algebraic proof and formal sum notation, preparing students for DP Analysis and Approaches. Standard Mathematics keeps the same core formulas but focuses more on applying them numerically, a better fit for students heading towards DP Applications and Interpretation.

Ask your child to explain the rule out loud before writing it down — if they can't say why a pattern works, they can't justify it on paper either, which is exactly what Criterion B marks. Practising with investigation-style questions, not just textbook drill sums, builds that explaining skill fastest.

Look for resources that mix short formula practice with full investigation-style questions requiring a general rule and justification, since that mirrors how Criterion B is actually marked. Topical worksheets and past-paper style investigations, marked against real MYP achievement level descriptors, are far more useful than generic sequence drill sheets.