Find a formula for the $n t h$ term of the following geometric sequence, then find the 4 th term of the sequence.
$7,28,112 , \ldots$
A) $a _ { n } = 7 ( 4 ) ^ { n } ; a _ { 4 } = 448$
B) $a _ { n } = 7 ( 4 ) ^ { n } ; a _ { 4 } = 1792$
C) $a _ { n } = 7 ( 4 ) ^ { n - 1 } ; a _ { 4 } = 1792$
D) $a _ { n } = 7 ( 4 ) ^ { n - 1 } ; a _ { 4 } = 448$
E) $a _ { n } = 7 ( 4 ) ^ { n - 1 } ; a _ { 4 } = 112$

Question

Quizplus · Accepted Answer

The formula for the $n$th 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, $a_1 = 7$ and $r = 4$, so $a_n = 7 \cdot 4^{(n-1)}$. The 4th term is $a_4 = 7 \cdot 4^{(4-1)} = 7 \cdot 4^3 = 7 \cdot 64 = 448$.

Find a Formula for The nthn t hnth Term of the Following Geometric Sequence, Then Find the 4

Find a Formula for The $n t h$ Term of the Following Geometric Sequence, Then Find the 4