Chapter 12 Sequences and Series - 12.3 Analyze Geometric Sequences and Series - 12.3 Exercises - Skill Practice - Page 814: 16

$a_n=6(3)^{n-1}$ and $a_7=4374$

Here, we have $6,18,54, 162$ This shows a geometric series with a common ratio of $6r=18 $ Thus, $r=3$ The nth term is given by $a_n= a_1 r^{n-1}$ This gives: $a_n=(6) \times (3)^{n-1}$ Plug in $n=7$ $a_7=6 \times (3)^{7-1}=4374$ Hence, $a_n=6(3)^{n-1}$ and $a_7=4374$