Unit 9
Sequences and series alongside the model-selection judgement that closes the course.
Lesson 9.1
An arithmetic sequence adds a fixed difference from one term to the next. A geometric sequence multiplies by a fixed ratio. For a nonzero geometric starting term, ratios between successive terms reveal the pattern; differences reveal arithmetic patterns. Sequence inputs are discrete integer positions.
Lesson 9.2
Choose a model using both the numerical pattern and the context. Equal first differences suggest a linear model, equal second differences at equally spaced inputs suggest a quadratic, and a constant positive output ratio suggests an exponential. A fitted pattern does not justify unlimited extrapolation.
Lesson 9.3
Technology can fit a model or approximate an intersection, but the result must still be interpreted with units, domain, and reasonable precision. A high fit statistic alone does not justify extrapolation far outside the data.
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