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Sequences and series practice

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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Check each sequence, evaluate the given formulas and write a formula from the first term and common ratio. 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 repeated multiplication with an explicit nth-term formula, including negative common ratios.

Worked example

The first term is 1.5 and the common ratio is -2. Find four terms and an explicit formula.

1.5, -3.0, 6.0, -12.0; a_n = 1.5 × (-2)^(n - 1).

Multiply by -2 at each step. Parentheses make the entire negative ratio the base of the power.

Teaching notes

Make the practice count

  • Check each consecutive ratio before calling a sequence geometric.
  • A negative ratio makes nonzero terms alternate signs.
  • The exponent is n - 1 because the first term requires no multiplication.
  • Tenths practice uses decimal first terms and integer ratios.

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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 SheetNameScoreTeacherDateGeometric SequencesComplete all three sections. Sequence indexing starts at 1.1. Is each list geometric? Give r when it is.1.3, -6, 13, -24Yes / No: ______ d or r: ______2.3.7, 22.2, 133.3, 799.2Yes / No: ______ d or r: ______3.4.2, 12.6, 37.8, 113.4Yes / No: ______ d or r: ______4.3, -9, 27, -81Yes / No: ______ d or r: ______2. Use the formula. Write the first four terms and the stated term.5.an= 4 · 6n - 1First 4: ________________a7= ________6.an= 2.4 · (-4)n - 1First 4: ________________a7= ________7.an= 2.4 · (-5)n - 1First 4: ________________a5= ________8.an= 3 · 5n - 1First 4: ________________a6= ________3. Use the first term and d or r. Write four terms and an explicit formula.9.a1= 3.5 r = -4First 4: ________________an= __________________10.a1= 4 r = 4First 4: ________________an= __________________11.a1= 4 r = 3First 4: ________________an= __________________12.a1= 1.7 r = -6First 4: ________________an= __________________math-sheet.comPage 1 of 1

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