An arithmetic sequence is defined by the explicit rule $a_n = 12 - 3(n-1)$. What is the correct recursive rule for this sequence?

$a_1 = 12$ and $a_n = a_{n-1} - 3$

$a_1 = -3$ and $a_n = a_{n-1} + 12$

$a_1 = 12$ and $a_n = a_{n-1} + 3$

$a_1 = 12$ and $a_n = -3 \cdot a_{n-1}$

A geometric sequence is given by the explicit formula $a_n = 6 \cdot 5^{n-1}$. Which of the following is the correct recursive rule for the sequence?

$a_1 = 6$ and $a_n = 5 \cdot a_{n-1}$

$a_1 = 5$ and $a_n = 6 \cdot a_{n-1}$

$a_1 = 6$ and $a_n = a_{n-1} + 5$

$a_1 = 5$ and $a_n = a_{n-1} + 6$

The first term is 15 and the common difference is 8.

The first term is 8 and the common difference is 15.

The first term is 15 and the common ratio is 8.

The first term is 8 and the common ratio is 15.