https://file.aiquickdraw.com/mathbot/file/1726552248219graigfxp.jpg

The question appears to be about a geometric sequence (barisan geometri) with the following information:

- \( U_1 = 8 \) (the first term)
- \( U_6 = \frac{1}{4} \) (the sixth term)

You are asked to find the common ratio \( r \) of the sequence.

In a geometric sequence, the general form for the \(n\)-th term is given by:

\[
U_n = U_1 \times r^{n-1}
\]

For the sixth term:

\[
U_6 = U_1 \times r^{6-1} = U_1 \times r^5
\]

Substituting the known values:

\[
\frac{1}{4} = 8 \times r^5
\]

To find \(r\), follow these steps:

1. Divide both sides of the equation by 8:
   \[
   r^5 = \frac{1}{4 \times 8} = \frac{1}{32}
   \]

2. Take the fifth root of both sides:
   \[
   r = \sqrt[5]{\frac{1}{32}} = \frac{1}{2}
   \]

Thus, the common ratio \( r \) is \( \frac{1}{2} \).

Would you like a more detailed explanation or have further questions?

Here are some related questions:
1. How do we find the sum of an infinite geometric series if the ratio \(r\) is between -1 and 1?
2. How does changing the first term \(U_1\) affect the whole sequence?
3. What is the formula for the sum of the first \(n\) terms in a geometric sequence?
4. Can you explain how to find the next term in a geometric sequence when given the first term and the ratio?
5. How do we determine whether a sequence is arithmetic or geometric?

**Tip**: Always check the ratio \(r\) carefully to see whether the sequence is converging or diverging!

Learn how to find the common ratio r in a geometric sequence where U1 = 8 and U6 = 1/4. This problem covers key concepts in geometric sequences and exponential equations, perfect for students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation