Write the nth term of the geometric sequence as a function of n. $$a _ { 1 } = 2 , a _ { k + 1 } = 4 a _ { k }$$
A) $a _ { n } = 2 ( 4 ) ^ { n - 1 }$
B) $a _ { n } = - 2 + 4 n$
C) $a _ { n } = 2 ( 4 ) ^ { n }$
D) $a _ { n } = 2 \left( \frac { 1 } { 4 } \right) ^ { n - 1 }$
E) $a _ { n } = 4 ( 2 ) ^ { n - 1 }$

Question

Quizplus · Accepted Answer

The given sequence is geometric with the first term $a_1 = 2$ and common ratio $r = 4$. The nth term of a geometric sequence is given by $a_n = a_1 \cdot r^{n-1}$, which simplifies to $a_n = 2 \cdot 4^{n-1}$.

Write the Nth Term of the Geometric Sequence as a Function