Sequences, exponential functions, and logarithms: a learning progression
Distinguish additive from multiplicative patterns and connect powers with logarithms.
Before you begin
Evaluate expressions and use exponents and function notation.
Readiness depends on the ideas you can use, not only your age or grade. Start earlier in the sequence when an example feels unfamiliar.
How the skill develops
- Identify the difference or ratio between consecutive terms.
- Write rules for arithmetic and geometric sequences.
- Interpret exponential growth and decay relative to an initial value.
- Use logarithms as inverse exponent questions and distinguish a term from a series sum.
What grade is this taught?
Our catalog includes this progression from grade 9 through grade 12. That is a map of the practice available here, not a rule that every school uses the same schedule. Earlier grades may introduce models that later grades formalize.
The sequence is our teaching organization, informed by the published curriculum reference. High-school courses and calculus enrollment vary; check your school’s syllabus for placement decisions.
Build your next practice steps
Mark skills you already feel comfortable with. We’ll suggest the next unchecked skills in this sequence. This is a self-selected path, not a test score.