Number Sequences — Going Further in MYP Year 5

Explore quadratic sequences, recursive rules, and arithmetic series sums in MYP Year 5. Build on arithmetic sequence foundations with more complex patterns.

Practice

Number Sequences 2

180 min100 marks

Start Test

✦

Want help mastering this topic?

Work 1-on-1 with an IB expert tutor.

Book a session →

Beyond Arithmetic: Extending Sequence Work

Having established arithmetic sequences and nth term formulas, this topic pushes further — exploring more complex patterns, sequences with variable differences, and problem types that require deeper structural reasoning.

Quadratic Sequences

A quadratic sequence has a constant second difference rather than a constant first difference. For example: 2, 5, 10, 17, 26 … has first differences 3, 5, 7, 9 and a second difference of 2. The general term follows a quadratic form: T_n = an² + bn + c. Students learn to find the values of a, b, and c by setting up a system of equations.

Sequences Defined Recursively

Some sequences are defined by a rule that links each term to the previous one — for example: T_n = T_n−1 + 2n. Students generate terms from these recurrence relations and may be asked to identify the pattern or write an explicit formula.

Applying Sequences to Real Contexts

More complex sequence problems at this level typically involve multi-stage modelling. A student might need to determine which term first exceeds a given value, or find the sum of the first n terms of an arithmetic sequence using S_n = n/2 × (2a + (n − 1)d).

Sum of an Arithmetic Sequence

Students extend their knowledge of arithmetic sequences to find the total of the first n terms. The formula S_n = n/2 × (first term + last term) connects naturally to what they already know, and is applicable in savings, construction, and scheduling contexts.

Common Challenges

Incorrectly identifying whether a sequence is arithmetic, quadratic, or neither
Errors in solving simultaneous equations when finding quadratic sequence coefficients
Applying the arithmetic sum formula to sequences that are not arithmetic

Frequently asked questions

Builds on basic linear and quadratic patterns from earlier in Unit 1 Number Standard. You tackle harder problems involving recursive rules (where each term depends on previous ones, like Fibonacci-style sequences), nested patterns, and figurate numbers. Word problems apply sequences to growth, savings, seating layouts, and tiling. Sits as the final sequence work in the Standard pathway, bridging into algebraic generalisation later in MYP.

Confusing recursive rules with closed-form (nth term) rules. A recursive rule like u(n+1) = u(n) + 3 needs the previous term, so you cannot jump straight to the 50th term without computing every step or converting it. In exams, always check whether the question gives u(n) in terms of n (closed form) or in terms of u(n-1) (recursive). Also write out the first three terms to verify your rule before committing.

Ready to start?

Book a free diagnostic.

Get started →