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Learning Goal
Part of: Build a function that models a relationship between two quantities — 5 of 5 cluster items
Write arithmetic and geometric sequences
HSF.BF.A.2
**HSF.BF.A.2**: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.
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HSF.BF.A.2: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.
What you'll learn
- Write an arithmetic sequence both recursively (a₁ = first term, aₙ = aₙ₋₁ + d) and explicitly (aₙ = a₁ + (n-1)d)
- Write a geometric sequence both recursively (a₁ = first term, aₙ = aₙ₋₁ · r) and explicitly (aₙ = a₁ · rⁿ⁻¹)
- Determine the common difference d (arithmetic) or common ratio r (geometric) from a sequence of terms
- Translate between recursive and explicit forms for both sequence types
- Use arithmetic and geometric sequences to model real-world situations (salary increases, depreciation, savings, population)
- Find a specific term of a sequence using the most efficient form (explicit for distant terms, recursive for sequential computation)
Prerequisites
Slides
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Slides
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