Math Problem Statement
how to get the ratio in geometric sequence
Solution
To find the ratio in a geometric sequence, follow these steps:
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Identify Two Consecutive Terms: Select any two consecutive terms in the sequence. Let's call the first term and the next term .
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Divide the Terms: Divide the later term by the earlier term. The formula to find the common ratio is:
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Simplify the Fraction: Simplify the result, if necessary, to get the common ratio .
Example:
Consider the geometric sequence: 2, 6, 18, 54,...
- Take two consecutive terms, say 6 and 2.
- Calculate the ratio:
- So, the common ratio is 3.
Would you like more details, or do you have any questions?
Here are 5 related questions:
- How do you find the nth term in a geometric sequence?
- What happens if the ratio in a geometric sequence is a fraction?
- How can you determine if a sequence is geometric?
- What is the sum of the first n terms of a geometric sequence?
- 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