State an explicit rule for the nth term of the recursively-defined sequence.
-$$a _ { n } = 8 \cdot a _ { n - 1 } ; a _ { 1 } = 2$$
A) $a _ { n } = 2 \cdot 8 ^ { n - 1 }$
B) $a _ { n } = 2 \cdot 8 ^ { n }$
C) $a _ { n } = 8 \cdot 2 ^ { n }$
D) $a _ { n } = 8 \cdot 2 ^ { n - 1 }$

Question

Quizplus · Accepted Answer

The sequence starts with $a_1 = 2$ and each term is 8 times the previous term ($a_n = 8 \cdot a_{n-1}$). This means each term is $2 \cdot 8^{n-1}$, where $n-1$ accounts for the initial term being multiplied by 8, $n-1$ times to reach the nth term.

State an Explicit Rule for the Nth Term of the Recursively-Defined