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Common ratio

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Algebra and Trigonometry

Definition

In a geometric sequence, the common ratio is the constant factor between consecutive terms. It is usually denoted by $r$ and can be found by dividing any term by its preceding term.

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5 Must Know Facts For Your Next Test

  1. The common ratio $r$ in a geometric sequence can be calculated using $r = \frac{a_{n+1}}{a_n}$, where $a_n$ is the n-th term.
  2. If the common ratio $|r| < 1$, the terms in the geometric sequence will get progressively smaller.
  3. If $|r| > 1$, the terms in the geometric sequence will grow exponentially.
  4. A geometric series with common ratio $r = 1$ has all terms equal, resulting in a constant sequence.
  5. For an infinite geometric series to converge, the common ratio needs to satisfy $|r| < 1$.

Review Questions

  • How do you calculate the common ratio of a geometric sequence?
  • What happens to a geometric sequence when the common ratio is greater than one?
  • Explain why an infinite geometric series converges for certain values of the common ratio.
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