Sequences and series
Geometric sequences worksheets
Identify geometric sequences, find common ratios, evaluate specified terms and write explicit formulas with integer or tenths first terms.
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Finite geometric series worksheets
Sum geometric lists, evaluate finite sigma notation and find the number of terms from a first term, last term and total. Choose integers, tenths or mixed practice.
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Add exactly the displayed terms, evaluate each finite geometric sum and use the given first term, last term and total to find the number of terms.
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From terms to a finite total
Each sheet has four finite-list sums, four sigma-notation sums and four questions about the number of terms. Choose integer, tenths or mixed practice.
Finite lists show exactly which terms to add. Sigma sums give both limits, and every number-of-terms question includes a first term, last term and total.
Learning objective
What this activity builds
Connect a common ratio, endpoints and term count with the total of a finite geometric series.
Worked example
Find the sum of the five terms 5, 10, 20, 40, 80.
155
Each term is twice the previous term. Add the five shown terms, or use 5 × (2^5 - 1) / (2 - 1) = 155.
Teaching notes
Make the practice count
- A finite list includes only the displayed terms.
- For a sum from n = 1, use a₁ × r^(n - 1).
- Put parentheses around a negative ratio before raising it to a power.
- For inverse questions, use r = (S - a₁) / (S - aₙ), then check both the last term and the total.
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Customize the practice
Choose your options, update the preview, then download the exact same pages.
Choose integers, tenths or mixed practice. Add finite lists, evaluate sigma notation and find the number of terms.
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Classify sequences from four terms or a formula as arithmetic, geometric or neither, with twelve questions and a separate answer key.
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