Number Sequences — Extended Level in MYP Year 5
Study geometric sequences and series in MYP Year 5 Extended Maths. Covers nth term, sum formulas, connection to exponential functions, and exam tips.
Geometric Sequences: A New Kind of Pattern
At Extended level, students move beyond arithmetic sequences to explore geometric sequences — sequences in which each term is obtained by multiplying the previous term by a constant called the common ratio (r). For example: 3, 6, 12, 24, 48 … has a common ratio of 2.
The nth Term of a Geometric Sequence
The general term is given by: Tn = a · rn−1
where a is the first term and r is the common ratio. Students use this formula to find specific terms, determine the position of a given term, and solve for unknown values of a or r when other information is provided.
Sum of a Geometric Series
The sum of the first n terms of a geometric sequence is:
Sn = a(rⁿ − 1)/(r − 1) for r ≠ 1
Students apply this in financial contexts (e.g. total investment returns), repeated percentage change, and any situation involving multiplicative accumulation.
Connecting Geometric Sequences to Exponential Functions
One of the most important insights at Extended level is that geometric sequences and exponential functions are deeply related. The nth term formula Tn = a · rn−1 has the same structure as f(x) = a · bx. This connection reinforces understanding of both topics and prepares students for DP-level analysis.
Comparing Arithmetic and Geometric Sequences
A recurring exam task involves identifying whether a given sequence is arithmetic, geometric, or neither. Students compare constant differences (arithmetic) against constant ratios (geometric) and must justify their classification with evidence from the sequence.
Common Errors
- Using the arithmetic nth term formula for a geometric sequence
- Misidentifying r when the sequence involves fractions or negative ratios
- Forgetting that the sum formula requires r ≠ 1 (when r = 1, it is simply Sn = na)
Criterion B Relevance
Geometric sequences lend themselves naturally to Criterion B tasks — students may be asked to identify a pattern, conjecture a general rule, and verify it. The structural elegance of the nth term formula and sum formula makes this topic well-suited to investigative work.