https://file.aiquickdraw.com/mathbot/file/1731953380558kh6y31ul.jpg

To solve this sequence problem:

### Rule:
The rule is given as:
\[
x_{n+1} = 3x_n + 8
\]

### Starting value:
\(x_1 = 4\)

### Step-by-step solution:

1. **Calculate \(x_2\):**
   Using the rule:
   \[
   x_2 = 3x_1 + 8 = 3(4) + 8 = 12 + 8 = 20
   \]

2. **Calculate \(x_3\):**
   Using the rule again:
   \[
   x_3 = 3x_2 + 8 = 3(20) + 8 = 60 + 8 = 68
   \]

### Final Answer:
\[
x_3 = 68
\]

Would you like further details or clarification on this? 

Here are five related questions to expand your understanding:
1. How would the sequence change if \(x_1\) were different?
2. Can you find a general formula for \(x_n\) based on \(n\)?
3. What happens if we use a different rule, like \(x_{n+1} = 2x_n + 5\)?
4. How would this sequence look if plotted on a graph?
5. Can you determine whether this sequence grows linearly or exponentially?

**Tip:** Always test a few terms in the sequence to ensure your calculations match the rule provided.

The rule to get from one term to the next in a sequence is x_{n+1} = 3x_n + 8. If x_1 = 4, work out the value of x_3.

Learn how to solve a recursive sequence where x_{n+1} = 3x_n + 8 and x_1 = 4. Detailed step-by-step solution provided to calculate x_3. Suitable for middle school math students.

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