Find an explicit rule for the nth term of the sequence.
-$4,12,36,108 , \ldots$
A) $a _ { n } = 3 \cdot 4 ^ { n - 1 }$
B) $a _ { n } = 4 \cdot 3 ^ { n }$
C) $a _ { n } = 4 \cdot 3 ^ { n - 1 }$
D) $a _ { n } = 4 \cdot 3 ^ { n + 1 }$

Question

Quizplus · Accepted Answer

The sequence is a geometric sequence where each term is 3 times the previous term, starting with 4. The formula for the nth term of a geometric sequence is $a_n = a_1 \cdot r^{n-1}$, where $a_1$ is the first term and $r$ is the common ratio. Here, $a_1 = 4$ and $r = 3$, so the explicit rule is $a_n = 4 \cdot 3^{n-1}$.

Find an Explicit Rule for the Nth Term of the Sequence