Write a formula for the general term (the nth term) of the geometric sequence.
-$2,6,18,54,162 , \ldots$
A) $a _ { n } = 2 ( 3 ) ^ { n - 1 }$
B) $a _ { n } = 2 ( 3 ) ^ { n }$
C) $a _ { n } = a _ { 1 } + 3 ^ { n }$
D) $a _ { n } = 2 ( 3 n )$

Question

Quizplus · Accepted Answer

The sequence is geometric with a common ratio of 3 (each term is 3 times the previous one), and the first term is 2. 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. Substituting $a_1 = 2$ and $r = 3$ gives $a_n = 2 \cdot 3^{(n-1)}$.

Write a Formula for the General Term (The Nth Term) 2,6,18,54,162,…2,6,18,54,162 , \ldots2,6,18,54,162,…

Write a Formula for the General Term (The Nth Term) $2,6,18,54,162 , \ldots$