We are given the recursive formula for a sequence:

$a_1 = 1 \quad \text{and} \quad a_n = 8a_{n-1} \quad \text{for } n \geq 2.$

Step-by-step calculations:

1. For $n = 2$: $a_2 = 8a_1 = 8 \times 1 = 8.$

2. For $n = 3$: $a_3 = 8a_2 = 8 \times 8 = 64.$

Final results:

$a_2 = 8, \quad a_3 = 64.$

Let me know if you'd like further clarifications! 😊

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Relative questions:

1. What is the general formula for $a_n$ in this sequence?
2. How would the sequence behave as $n \to \infty$?
3. Can this sequence be represented graphically? What would it look like?
4. How does the growth rate of this sequence compare to a linear or quadratic sequence?
5. What happens if $a_1$ is changed to a different value, e.g., $a_1 = 2$?

Tip:

For recursive sequences, always compute a few terms manually first to observe patterns before deriving general results.