Conversion and Sequences – MYP Year 5 Extended Algebra
Learn recursive and explicit sequence representations for MYP Year 5 Extended algebra. Understand how to convert between forms and apply them accurately.
What This Topic Is About
Conversion and Sequences deals with how the same sequence can be represented in different ways — and how to move between those representations accurately. This skill underpins all the other sequence topics in Unit 2 Extended.
Types of Sequence Representation
Recursive Form
A recursive formula defines each term by reference to the one before it. For example: u₁ = 3, uₙ = uₙ₋₁ + 4. This is intuitive to generate but impractical if you want the 100th term without listing all the ones before it.
Explicit (General) Form
An explicit formula gives the nth term directly in terms of n — for example, uₙ = 4n − 1. Students need to be able to derive an explicit formula from a recursive one, and vice versa, and to verify that both forms produce the same sequence.
What Students Are Expected to Do
- Identify whether a given formula is recursive or explicit
- Generate the first several terms from each type
- Convert a recursive rule into explicit form using algebraic reasoning
- Explain why explicit forms are more useful for large values of n
MYP Question Style
Questions often provide a partially completed sequence or a table of values and ask students to write both representations. Criterion A questions expect accuracy; Criterion C questions expect students to explain their reasoning in words as well as symbols.
Common Mistakes
- Confusing the first term index (some sequences are defined from n = 0, others from n = 1)
- Writing a recursive rule that works for the numbers given but is mathematically incomplete (no base case)
- Incorrectly identifying a non-linear sequence as arithmetic when converting