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tentukan suku ke-10 dari barisan bilangan 90,45, 45

The problem asks to find the 10th term in the sequence that starts with: 

\[ 90, 45, \frac{45}{2}, \frac{45}{4}, \frac{45}{8}, \dots \]

### Identifying the Sequence:

From the given terms, the pattern suggests that each term is halved successively after the second term:

- \( 90 \)
- \( 45 \) 
- \( \frac{45}{2} \)
- \( \frac{45}{4} \)
- \( \frac{45}{8} \)

This indicates that the common ratio between consecutive terms is \( \frac{1}{2} \), forming a geometric sequence after the first two terms.

### General Formula for the Sequence:

The first term (\( a_1 \)) is \( 90 \), and the second term (\( a_2 \)) is \( 45 \). The terms after the second follow the form of:

\[
a_n = 45 \times \left(\frac{1}{2}\right)^{n-2} \quad \text{for} \, n \geq 2
\]

### Finding the 10th Term:

Now, we want to find the 10th term. For \( n = 10 \):

\[
a_{10} = 45 \times \left(\frac{1}{2}\right)^{10-2} = 45 \times \left(\frac{1}{2}\right)^8
\]

\[
a_{10} = 45 \times \frac{1}{256} = \frac{45}{256}
\]

Thus, the 10th term of the sequence is \( \frac{45}{256} \).

Let me know if you need any further explanation or more details.

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### Related Questions:
1. What is the 5th term in this sequence?
2. How do you determine if a sequence is geometric?
3. What is the sum of the first 10 terms in this geometric sequence?
4. How does the common ratio affect the behavior of a geometric sequence?
5. Can this sequence have a limit as \( n \) approaches infinity?

### Tip:
In geometric sequences, if the common ratio is less than 1, the terms approach 0 as \( n \) increases.

Tentukan suku ke-10 dari barisan bilangan 90, 45, 45/2, 45/4, 45/8, ...

Learn how to find the 10th term in the geometric sequence that begins with 90, 45, 45/2, ... by applying the general term formula for geometric sequences. Suitable for students in Grades 9-11.

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