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Sequences and series practice

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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Check each sequence, evaluate the given formulas and write a formula from the first term and common difference. Start with n = 1.

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Connect the pattern with its formula

Each worksheet has twelve questions: identify a sequence, use an explicit formula to calculate terms, and build a formula from the first term and its common difference or ratio.

Choose integers, tenths or a balanced mix. Terms may be negative. Geometric practice uses integer common ratios, with parentheses around negative bases.

Learning objective

What this activity builds

Connect a constant difference with sequence terms and an explicit nth-term formula.

Worked example

The first term is 5 and the common difference is -3. Find four terms and an explicit formula.

5, 2, -1, -4; a_n = 5 - 3(n - 1) = 8 - 3n.

Subtract 3 for each new term. There are n - 1 steps from the first term to the nth term.

Teaching notes

Make the practice count

  • Check every consecutive difference before calling a sequence arithmetic.
  • Substitute n = 1 to check that a formula returns the first term.
  • Keep a negative difference when the sequence decreases.
  • Use tenths practice to connect decimal arithmetic with algebra.

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Customize the practice

Choose your options, update the preview, then download the exact same pages.

Choose integer, tenths or mixed practice. Each sheet has four classification, four term-evaluation and four formula-writing questions.

Worksheet settings

Integer practice may include negative results. Tenths are shown with exactly one decimal place.

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Math SheetNameScoreTeacherDateArithmetic SequencesComplete all three sections. Sequence indexing starts at 1.1. Is each list arithmetic? Give d when it is.1.11, 10, 12, 8Yes / No: ______ d or r: ______2.8, 17, 27, 35Yes / No: ______ d or r: ______3.17.5, 20.7, 23.9, 27.1Yes / No: ______ d or r: ______4.23.6, 16.9, 10.2, 3.5Yes / No: ______ d or r: ______2. Use the formula. Write the first four terms and the stated term.5.an= 23.4 - 5.9nFirst 4: ________________a6= ________6.an= 30 + 2nFirst 4: ________________a18= ________7.an= 17 - 9nFirst 4: ________________a15= ________8.an= 9.2 + 1.3nFirst 4: ________________a12= ________3. Use the first term and d or r. Write four terms and an explicit formula.9.a1= 25.3 d = 7.1First 4: ________________an= __________________10.a1= 6 d = -9First 4: ________________an= __________________11.a1= 9.9 d = -6.1First 4: ________________an= __________________12.a1= 15 d = 2First 4: ________________an= __________________math-sheet.comPage 1 of 1

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