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Learning Goal
Part of: Write expressions in equivalent forms to solve problems — 2 of 2 cluster items
Derive geometric series formula
HSA.SSE.B.4
**HSA.SSE.B.4**: Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems. For example, calculate mortgage payments.
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HSA.SSE.B.4: Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems. For example, calculate mortgage payments.
What you'll learn
- Identify a geometric series and state the first term, common ratio, and number of terms
- Derive the formula S = a(1 - r^n)/(1 - r) using the multiply-and-subtract technique, and explain each step of the derivation
- Apply the formula to compute the sum of any finite geometric series where r != 1
- Handle the special case r = 1 correctly (sum = na) and explain why the main formula cannot be used when r = 1
- Solve real-world problems (savings plans, loan payments, repeated geometric growth) using the geometric series formula
Prerequisites
Slides
Interactive presentations perfect for visual learners • 2 slide decks
Slide Video
Watch narrated slides play like a video lesson • Narrated slide playback
Task-sets
Learning resource • 2 task-setss