Defining sequences as functions

The  exercise appears under the Precalculus Math Mission. This exercise view sequences as functions.

Types of Problems
There are two types of problems in this exercise:


 * 1) Find the numbers to define the function recursively: This problem provides a T-table with various values of a function. The student is asked to find values for constants to define the function recursively.Dsaf1.png
 * 2) Find the numbers to define the function explicitly: This problem provides a T-table with various values of a function. The student is asked to find values for constants to define the function explicitly.Dsaf2.png

Strategies
Knowledge of arithmetic and geometric sequences, as well as function notation and application, are encouraged to ensure success on this exercise.
 * 1) Arithmetic sequences (with common differences) and geometric sequences (with common ratios) can both show up on this exercise.
 * 2) Recursive functions are defined in terms of previously given values, whereas explicit formulas allow one to jump to the final answer.
 * 3) 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

 * 1) Sequences as functions are foundational in discrete mathematics, the math of much of computer science.
 * 2) Functions are able to be written into TI80 level calculators.