Chapter 12 Sequences and Series - 12.3 Analyze Geometric Sequences and Series - 12.3 Exercises - Skill Practice - Page 814: 18

$a_n=7 (-5)^{n-1}$ and $a_7=109375$

The nth term is given by $a_n= a_1 r^{n-1}$ Here, $a_1=7; r=\dfrac{a_2}{a_1}=\dfrac{-35}{7}=-5$ $a_n=(7) \times (-5)^{n-1}$ This gives: $a_n=7 (-5)^{n-1}$ Plug in $n=7$ $a_7=7 \times (-5)^{7-1}=109375$ Hence, $a_n=7 (-5)^{n-1}$ and $a_7=109375$