Evidence of Understanding

**compare a variety of sequences and describe how to extend each sequence**- describe the relationship between the term of a sequence and the number in the sequence
*Example: In the sequence 3, 5, 7, 9,... the first term is the number 3, the third term is 7, etc.*

- determine when a sequence can be generated by a consistent pattern and describe the pattern
- describe an
**arithmetic**sequence using the**common difference** - describe a
**geometric**sequence using the**common ratio**or**multiplier**

- describe an
- use the common difference or ratio to find missing values in the sequence

- describe the relationship between the term of a sequence and the number in the sequence
**represent a sequence with a visual diagram or graph**- explain why the graph of a sequence is always
**discrete** - use rate of change to justify why geometric sequences are modeled by exponential functions
- connect the common difference of an arithmetic sequence with the constant rate of change for a linear function
- connect the common ratio of a geometric sequence with the constant factor of change for an exponential function

- analyze a visual or graph to determine if a given value belongs in the sequence

- explain why the graph of a sequence is always
**create an explicit or recursive rule for an arithmetic or geometric sequence**- use a function rule to determine if a value belongs in an arithmetic or geometric sequence
- generate a rule from a situation, graph, table, or visual
- given non consecutive values in an arithmetic or geometric sequence, create and justify an
**explicit**rule

- given non consecutive values in an arithmetic or geometric sequence, create and justify an
- compare and convert between the explicit and
**recursive**rules for a sequence

Develop conceptual understanding:

arithmetic, geometric, common difference, common ratio, multiplier, discrete, explicit, recursive

Supporting terms to communicate:

term, linear, exponential, rate of change, initial value, coefficient, constant, base, exponent, integer, consecutive