Math Problem Statement
Instructions: Find the common ratio of the geometric sequence. Write your answer as a fraction. Use a forward slash (i.e. "/") for all fractions (e.g. 1/2 for 1/2).
1,1/2,1/4,1/8,1/16
Common Ratio:
Solution
The common ratio in a geometric sequence is found by dividing any term by its previous term.
For this sequence:
1, 1/2, 1/4, 1/8, 1/16
Take the second term and divide it by the first term:
Now, let's check the ratio between the next terms to confirm consistency:
The common ratio is:
Would you like more details or have any further questions?
Here are 5 related questions:
- What is the 10th term of this geometric sequence?
- How do you find the sum of an infinite geometric series?
- What is the general formula for the nth term in a geometric sequence?
- Can the common ratio in a geometric sequence be negative?
- What happens to a geometric sequence if the common ratio is greater than 1?
Tip: In a geometric sequence, the common ratio is constant between any two consecutive terms.
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Math Problem Analysis
Mathematical Concepts
Geometric Sequences
Ratios
Fractions
Formulas
Common ratio formula: r = a_n / a_(n-1)
Theorems
Geometric Sequence Properties
Suitable Grade Level
Grades 6-8
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