# 8: Problem Solving

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## Learning Objectives

• Recognize and distinguish between arithmetic, geometric, and quadratic sequences.
• Create a general term for arithmetic, geometric, and quadratic sequences.
• Recognize a pattern and infer the pattern on subsequent terms of a sequence.
• Identify a sequence pattern within real-life observations.

• 8.1: Arithmetic Sequences
We can describe a sequence in words (e.g. a sequence of even numbers.) but can we describe the sequence mathematically? That is, can we describe the pattern of the sequence of even numbers using a formula? Absolutely! This section will explore arithmetic sequences, how to identify them, mathematically describe their terms, and the relationship between arithmetic sequences and linear functions. Let’s get started!
• 8.2: Problem Solving with Arithmetic Sequences
Arithmetic sequences, introduced in Section 8.1, have many applications in mathematics and everyday life. This section explores those applications.
• 8.3: Geometric Sequences
Geometric sequences have a common ratio. Each term after the first term is obtained by multiplying the previous term by r, the common ratio. As an example, the following sequence does not have a common difference, so it is not an arithmetic sequence.