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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.
    • 8.4: Quadratic Sequences
      Quadratic functions are polynomial functions of degree two. For example, f(x) = x^2 is a quadratic function. This section will explore patterns in quadratic functions and sequences. Identifying patterns within a function table gives us valuable clues to build the right function to match the mathematical pattern.

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    This page titled 8: Problem Solving is shared under a CC BY-SA 4.0 license and was authored, remixed, and/or curated by Jennifer Freidenreich.

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