Romeo was asked to evaluate the common ratio of 4, 1, ¼, ¹/16, .... . Whisch is his common ratio?

The sequence given is: 4, 1, ¼, ¹/16, ....

This is a geometric sequence, and the common ratio (r) can be found by dividing any term by its preceding term.

Let's calculate the common ratio:

1. From 4 to 1:
   \[
   r = \frac{1}{4} = \frac{1}{4}
   \]

2. From 1 to \( \frac{1}{4} \):
   \[
   r = \frac{\frac{1}{4}}{1} = \frac{1}{4}
   \]

3. From \( \frac{1}{4} \) to \( \frac{1}{16} \):
   \[
   r = \frac{\frac{1}{16}}{\frac{1}{4}} = \frac{1}{16} \times \frac{4}{1} = \frac{1}{4}
   \]

Thus, the common ratio is \( \frac{1}{4} \).

Would you like further details or have any questions?

Here are 5 related questions:

1. How do you find the nth term of a geometric sequence?
2. What is the sum of an infinite geometric series?
3. How can you differentiate between arithmetic and geometric sequences?
4. How do you find the first term of a geometric sequence if the common ratio and another term are known?
5. What is the formula for the sum of a finite geometric series?

**Tip**: Always double-check the ratio by dividing consecutive terms to ensure accuracy in geometric sequences.

Romeo was asked to evaluate the common ratio of 4, 1, ¼, ¹/16, .... . What is his common ratio?

Learn how to find the common ratio of the geometric sequence 4, 1, ¼, ¹/16. This step-by-step solution uses the formula r = a_(n+1) / a_n to calculate the ratio. Ideal for students in Grades 9-10 who are studying sequences and series.

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