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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Arithmetic and geometric means worksheets
Insert one, two or three missing terms between endpoints of arithmetic and geometric sequences. Choose positive, negative or mixed numbers with twelve questions and separate answer keys.
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Find the missing terms in each sequence. Use a positive common ratio for every geometric sequence.
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Fill the gaps between two endpoints
Each sheet has six arithmetic sequences and six geometric sequences. Choose positive, negative or mixed numbers and any combination of one, two or three missing terms.
Use equal differences for arithmetic sequences and a positive common ratio for geometric sequences. Answer keys list the missing terms in order and show the difference or ratio.
Learning objective
What this activity builds
Use equal differences or equal positive ratios to find the missing terms between two endpoints.
Worked example
Insert two arithmetic means between 3 and -9.
-1 and -5
Two missing terms create three equal steps. The common difference is (-9 - 3) / 3 = -4, giving 3, -1, -5, -9.
Teaching notes
Make the practice count
- There is one more step than the number of missing terms.
- For arithmetic means, divide the endpoint difference by the number of steps.
- For geometric means, find a positive ratio whose repeated multiplication reaches the last term.
- Check every consecutive difference or ratio, including the steps to both endpoints.
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Choose the number signs and how many terms to fill in. Geometric questions use a positive common ratio, including when all terms are negative.
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