The Modeling with sequences exercise appears under the Precalculus Math Mission and Mathematics III Math Mission. This exercise uses word problems to practice recognizing the difference between arithmetic and geometric sequences, and recursive and explicit definitions.
Types of Problems[]
There are two types of problems in this exercise:
- Determine type of sequence and define recursively: This problem provides a context-based problem. The user is asked to determine if the relationship is arithmetic or geometric, then find values for constants to define the function recursively.
Determine type of sequence and define recursively
- Determine type of sequence and define explicitly: This problem provides a context-based problem. The user is asked to determine if the relationship is arithmetic or geometric, then find values for constants to define the function recursively.
Determine type of sequence and define explicitly
Strategies[]
Knowledge of arithmetic and geometric sequences, as well as function notation and application, are encouraged to ensure success on this exercise.
- Arithmetic sequences (with common differences) and geometric sequences (with common ratios) can both show up on this exercise.
- Recursive definitions are in terms of previously given values, whereas explicit formulas allow one to jump to the final answer.
- Accuracy can be completed on this exercise by checking the function found and seeing if the results align with the T-table.
Real-life Applications[]
- Sequences are foundational in discrete mathematics, the math of much of computer science.
- The problems in this exercise are real-life applications that model situations.