What is 10th term of geometric sequence 8,4,2,1,...?

To find the 10th term of a geometric sequence, you can use the formula:

\[
a_n = a_1 \times r^{(n-1)}
\]

where:
- \( a_n \) is the \( n \)-th term of the sequence,
- \( a_1 \) is the first term,
- \( r \) is the common ratio,
- \( n \) is the term number.

Given:
- \( a_1 = 8 \),
- The common ratio \( r = \frac{4}{8} = \frac{1}{2} \),
- \( n = 10 \).

Now, plug in the values:

\[
a_{10} = 8 \times \left(\frac{1}{2}\right)^{(10-1)} = 8 \times \left(\frac{1}{2}\right)^9 = 8 \times \frac{1}{512} = \frac{8}{512} = \frac{1}{64}
\]

So, the 10th term of the sequence is \( \frac{1}{64} \).

Would you like further details or have any questions? 

Here are some related questions:
1. How do you find the common ratio in a geometric sequence?
2. What is the sum of the first 10 terms of this geometric sequence?
3. How do you determine if a sequence is arithmetic or geometric?
4. What is the general formula for the sum of an infinite geometric series?
5. How does changing the common ratio affect the sequence?

**Tip:** In a geometric sequence, if the common ratio is a fraction between 0 and 1, the terms will get smaller as the sequence progresses.

Learn how to find the 10th term of the geometric sequence 8, 4, 2, 1, ... using the geometric sequence formula. Understand the concept of common ratio and its application in sequences. Suitable for students in Grades 9-12.

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