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.