Sequences and series
Arithmetic series worksheets
Sum finite arithmetic lists, evaluate sigma notation and find the number of terms from a first term, last term and total. Choose integers or tenths.
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General series worksheets
Expand sigma notation into finite sums, evaluate polynomial and exponential series, and rewrite sums in sigma notation. Combine the three problem types in twelve-question worksheets.
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Expand, evaluate or rewrite each finite series as directed. Include both the lower and upper index when listing terms.
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Connect terms with sigma notation
Choose any combination of expanding sums, evaluating series and writing sigma notation. Each twelve-question sheet includes linear, quadratic and exponential expressions.
Both index limits are inclusive. Answer keys show every expanded term, an exact total or one possible sigma expression. Equivalent formulas that reproduce the same terms are also valid.
Learning objective
What this activity builds
Connect a finite sum with its indexed formula and inclusive limits, then evaluate the terms exactly.
Worked example
Expand and evaluate the sum of n² for n = 1 through 4.
1 + 4 + 9 + 16 = 30
Substitute each integer index, including both endpoints, then add the four resulting terms.
Teaching notes
Make the practice count
- Read the lower index before substituting; some sums start at zero.
- Count the terms as upper index minus lower index plus one.
- Evaluate powers before adding the terms.
- Equivalent sigma expressions can use different formulas and limits; check every term in order.
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Customize the practice
Choose your options, update the preview, then download the exact same pages.
Choose one, two or all three problem types. Expand finite sums, evaluate exact totals and write sigma notation, including series that start at zero.
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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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Comparing arithmetic and geometric sequences worksheets
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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