Sequences and series
Arithmetic sequences worksheets
Identify arithmetic sequences, find common differences, evaluate specified terms and write explicit formulas with integer or tenths practice.
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General sequences worksheets
Continue number patterns, write explicit and recursive sequence formulas, and find the first four terms from a given rule. Practice linear, quadratic and exponential patterns.
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Use a simple pattern that fits all four terms. Give the requested continuation or formulas, then find the first four terms from each given rule.
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Connect a pattern with its rule
For six term lists, choose any combination of finding the next three terms, an explicit formula and a recursive formula. For six given formulas, find the first four terms.
Choose explicit, recursive or mixed given formulas. Patterns include linear, quadratic and exponential rules. Recursive rules include an initial value; answer keys show one possible simple pattern and accept equivalent formulas.
Learning objective
What this activity builds
Connect a sequence of terms with an explicit formula and an initialized recursive rule.
Worked example
Find a rule for 3, 9, 21, 39 and continue the next three terms.
63, 93, 129; one rule is a_n = 3 + 6n(n - 1)/2.
The differences are 6, 12 and 18, increasing by 6 each time. Equivalently, start at a₁ = 3 and add 6(n - 1) at step n for n ≥ 2.
Teaching notes
Make the practice count
- An explicit formula finds a term directly from its index.
- A recursive rule needs an initial term and tells how to get the next term.
- Start at n = 1 when finding the first four terms.
- Check every supplied term, including the first, before accepting a formula.
- A finite list can fit more than one rule; the answer key gives one intended simple pattern.
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Choose your options, update the preview, then download the exact same pages.
Choose what to find from the term lists, then choose the format of the given formulas. Formula questions always ask for the first four terms, starting at n = 1.
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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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Sequences and series
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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