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Sequences & Series · Sequences

Geometric Sequence

an=a1⋅rn−1a_n = a_1 \cdot r^{n-1}

Each term is obtained by multiplying the previous term by a constant ratio r. Converges if |r| < 1.

  • 2 worked examples
  • 18 in Sequences & Series

Worked examples

Find the 6th term of the geometric sequence with a₁ = 3, r = 2.
  1. a₆ = 3 · 2⁵ = 3 · 32 = 96

Answer: 96

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Does {(2/3)ⁿ} converge?

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Related formulas

Geometric Series

See all 18 Sequences & Series formulas on one printable sheet - the same statements and conditions as these pages, typeset and laid out for paper.

Common questions

What is the Geometric Sequence?

Each term is obtained by multiplying the previous term by a constant ratio r. Converges if |r| < 1. It is one of the sequences & series formulas in the CalcRef reference.

How do you use the Geometric Sequence?

Worked example. Find the 6th term of the geometric sequence with a₁ = 3, r = 2. a₆ = 3 · 2⁵ = 3 · 32 = 96. Answer: 96.

Practice

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