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:

1/21=1/2\frac{1/2}{1} = 1/2

Now, let's check the ratio between the next terms to confirm consistency:

1/41/2=1/2,1/81/4=1/2,1/161/8=1/2\frac{1/4}{1/2} = 1/2, \quad \frac{1/8}{1/4} = 1/2, \quad \frac{1/16}{1/8} = 1/2

The common ratio is:

1/2\boxed{1/2}

Would you like more details or have any further questions?

Here are 5 related questions:

  1. What is the 10th term of this geometric sequence?
  2. How do you find the sum of an infinite geometric series?
  3. What is the general formula for the nth term in a geometric sequence?
  4. Can the common ratio in a geometric sequence be negative?
  5. 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