Curriculum placement
Algebra 1. This describes the skill, not a learner estimate.
Rules for an arithmetic sequence
Translate arithmetic sequences between recursive and explicit rules
Problem types
- Arithmetic sequences
- Arithmetic sequence as a function
- Arithmetic series and recursive rules
- Find a term of a sequence defined by a nonlinear recursive rule
- Find a distant term of an arithmetic sequence from its listed terms
- Show the work: terms of a recursive sequence
Builds on
- Linear models of a situation
- Two patterns on one graph
- Patterns in the operations · Earlier idea
A pattern that adds the same number each time is an arithmetic sequence, written with a first term and a common difference.
Leads to
- Motion described by a parameter · See it applied
Position after equal steps is a first term plus a number of common differences, as a parametric equation moves at constant velocity.
Related skills
- Linear growth against exponential growth · Related idea
An arithmetic sequence adds a constant each step and a geometric sequence multiplies. Comparing them shows linear against exponential growth.
- Sums of a finite geometric sequence · Related idea
An arithmetic series adds terms that change by a fixed amount, so pairing first and last terms gives its sum. A geometric series adds terms that change by a fixed ratio and uses a different sum rule.
- Linear equations from constraints · Shared foundations
- Reading slope and intercept in context · Shared foundations
- Scatter plots and trend lines · Shared foundations
Open the interactive map to explore lessons and skill connections.