IM Alg2.1.5 Lesson: Sequences are Functions
Describe how to produce one step of the pattern from the previous step.
Here is a visual pattern of dots.
The number of dots is a function of the step number .
What values make sense for in this situation?
What values don't make sense for ?
Complete the table for Steps 1 to 5.
Following the pattern in the table, write an equation for in terms of the previous step. Be prepared to explain your reasoning.
Consider the same triangular pattern.
Is the sequence defined by the number of dots in each step arithmetic, geometric, or neither? Explain how you know.
Can you write an expression for the number of dots in Step without using the value of from a previous step?
Use the first 5 terms of each sequence to state if the sequence is arithmetic, geometric, or neither.
Next, define the sequence recursively using function notation.