Chapter 12 Sequences and Series - 12.3 Analyze Geometric Sequences and Series - 12.3 Exercises - Skill Practice - Page 814: 17

$a_n=4(6)^{n-1}$ and $a_7=186624$

The given series shows a geometric series with a common ratio $4r=24 $ Thus, $r=6$ The nth term is given by $a_n= a_1 r^{n-1}$ This gives: $a_n=(4) \times (6)^{n-1}$ Plug in $n=7$ $a_7=4 \times (6)^{7-1}=186624$ Hence, $a_n=4(6)^{n-1}$ and $a_7=186624$