#### Math - 2017-18

# 6.17 - Sequences

**6.17** The student will **identify **and **extend **geometric
and arithmetic sequences.

**Bloom's Level:** Understand Apply

*Adopted: 2009*

### BIG IDEAS

- I can crack a secret code, figure compound interest, and
determine a retirement salary if given the same raise each year.

- I will recognize that patterns exhibit relationships that can be extended, described, and generalized.

### UNDERSTANDING THE STANDARD

- Numerical patterns may include linear and
exponential growth, perfect squares, triangular and other polygonal numbers, or
Fibonacci numbers.
- Arithmetic and geometric sequences are types of
numerical patterns.
- In the numerical pattern of an arithmetic sequence,
students must determine the difference, called the common difference, between each succeeding number in order to
determine what is added to each previous number to obtain the next number.
Sample numerical patterns are 6, 9, 12, 15, 18, …; and 5, 7, 9, 11, 13, …
- In geometric number patterns, students must
determine what each number is multiplied by to obtain the next number in the
geometric sequence. This multiplier is called the common ratio. Sample geometric number patterns include 2, 4, 8, 16,
32, …; 1, 5, 25, 125, 625, …; and 80, 20, 5, 1.25, …
- Strategies to recognize and describe the
differences between terms in numerical patterns include, but are not limited
to, examining the change between consecutive terms, and finding common factors.
An example is the pattern 1, 2, 4, 7, 11, 16, …

### ESSENTIALS

- What is the difference between an arithmetic and
a geometric sequence?

While both are numerical patterns, arithmetic sequences are additive and geometric sequences are multiplicative.

**The student will use problem solving, mathematical
communication, mathematical reasoning, connections, and representations to**

6.17_{1} **Investigate **and **apply **strategies to recognize
and describe the change between terms in
arithmetic patterns.

6.17_{2} **Investigate **and **apply** strategies to recognize
and describe geometric patterns.

6.17_{3} **Describe **verbally and in writing the
relationship between consecutive terms in an arithmetic or geometric sequence.

6.17_{4} **Extend **and **apply **arithmetic and geometric
sequences to similar situations.

6.17_{5} **Extend **arithmetic and geometric sequences in
a table by using a given rule or mathematical relationship.

6.17_{6} **Compare **and **contrast **arithmetic and geometric
sequences.

6.17_{7} **Identify **the common difference for a given
arithmetic sequence.

6.17_{8} **Identify **the common ratio for a given
geometric sequence.

### KEY VOCABULARY

geometric sequence, arithmetic sequence, numerical pattern, linear
growth, exponential growth, consecutive terms

*Updated: Jun 06, 2017*