Answer
(a.)
$a_1=14;a_n=a_{n-1}\cdot 6$
$a_n=14\cdot 6^{n-1}$
$a_8=3919,104$
(b.)
$a_1=648;a_n=a_{n-1}\cdot \frac{1}{2}$
$a_n=648\cdot (\frac{1}{2})^{n-1}$
$a_8=5.0625$
Work Step by Step
(a.)
First term $a_1=14$.
Common ratio $r=\frac{84}{14}=6$.
The recursive formula is
$a_1=a;a_n=a_{n-1}\cdot r$
$a_1=14;a_n=a_{n-1}\cdot 6$
The explicit formula is
$a_n=a_1\cdot r^{n-1}$
$a_n=14\cdot 6^{n-1}$
The $8th$ term is
$a_8=14\cdot 6^{8-1}$
Simplify.
$a_8=14\cdot 6^{7}$
$a_8=3919,104$
(b.)
First term $a_1=648$.
Common ratio $r=\frac{324}{648}=\frac{1}{2}$.
The recursive formula is
$a_1=a;a_n=a_{n-1}\cdot r$
$a_1=648;a_n=a_{n-1}\cdot \frac{1}{2}$
The explicit formula is
$a_n=a_1\cdot r^{n-1}$
$a_n=648\cdot (\frac{1}{2})^{n-1}$
The $8th$ term is
$a_8=648\cdot (\frac{1}{2})^{8-1}$
Simplify.
$a_8=648\cdot (\frac{1}{2})^{7}$
$a_8=5.0625$
