https://file.aiquickdraw.com/mathbot/file/1727026260194yiusozer.jpg

From the image you've uploaded, I can see two math problems. Let's address them one by one:

### Problem 1:
**What is the fifth term in the series: 5 : 2 : 9 : 6 : ?**
- The pattern alternates between two different sequences.
  - First sequence (odd positions): 5, 9, ?
  - Second sequence (even positions): 2, 6
  
  For the first sequence:
  - The difference between 5 and 9 is \( +4 \), so adding 4 to 9 gives the next term as \( 13 \).

  The fifth term in the sequence is **13**.

### Problem 2:
**In a theater audience of 500 people, 80% were adults. How many adults were in the audience?**
- To find the number of adults, calculate 80% of 500:
  \[
  \text{Number of adults} = \frac{80}{100} \times 500 = 0.8 \times 500 = 400
  \]
  
  There are **400 adults** in the audience.

Would you like more details on these solutions or have further questions? 

Here are 5 related questions:
1. How would you find the sum of an alternating sequence like this one?
2. Can you create a pattern that alternates increasing and decreasing terms?
3. What if only 70% of the audience were adults, how many would that be?
4. How can you express the pattern rule algebraically for a general term?
5. If the theater had 600 people, what would 80% of the audience be?

**Tip:** When dealing with sequences, always look for consistent patterns in either differences, ratios, or other operations between terms.

What is the fifth term in the series: 5 : 2 : 9 : 6 : ?; In a theater audience of 500 people, 80% were adults. How many adults were in the audience?

Learn how to find the fifth term in the sequence 5, 2, 9, 6 and how to calculate the percentage of adults in a theater audience. This problem covers arithmetic sequence and percentage calculations. Suitable for Grades 6-8.

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