Math Problem Statement

how to get the ratio in geometric sequence

Solution

To find the ratio in a geometric sequence, follow these steps:

  1. Identify Two Consecutive Terms: Select any two consecutive terms in the sequence. Let's call the first term ana_n and the next term an+1a_{n+1}.

  2. Divide the Terms: Divide the later term by the earlier term. The formula to find the common ratio rr is: r=an+1anr = \frac{a_{n+1}}{a_n}

  3. Simplify the Fraction: Simplify the result, if necessary, to get the common ratio rr.

Example:

Consider the geometric sequence: 2, 6, 18, 54,...

  • Take two consecutive terms, say 6 and 2.
  • Calculate the ratio: r=62=3r = \frac{6}{2} = 3
  • So, the common ratio rr is 3.

Would you like more details, or do you have any questions?


Here are 5 related questions:

  1. How do you find the nth term in a geometric sequence?
  2. What happens if the ratio in a geometric sequence is a fraction?
  3. How can you determine if a sequence is geometric?
  4. What is the sum of the first n terms of a geometric sequence?
  5. How does the common ratio affect the behavior of a geometric sequence?

Tip: If the ratio is less than 1, the terms in the sequence will decrease over time, but if the ratio is greater than 1, the terms will increase.

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Math Problem Analysis

Mathematical Concepts

Geometric Sequences

Formulas

Formula to find the common ratio in a geometric sequence

Theorems

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Suitable Grade Level

Grades 9-12