Exercise 48 Page 345

We are asked to write the $2^{\text{nd}},$ $5^{\text{th}}$ and $10^{\text{th}}$ term of a sequence, given a recursive rule. To do so, we will use a table.

$n$	$f(n)=6f(n-1)$	$f(n)$
$1$	$f(1)=\text{-}1$	$\text{-}1$
$2$	$f(2)=6f(2-1)$ $\Updownarrow$ $f(2)=6f(1)$	$f(2)=6(\text{-}1)$ $\Updownarrow$ $f(2)=\text{-}6$
$3$	$f(3)=6f(3-1)$ $\Updownarrow$ $f(3)=6f(2)$	$f(3)=6(\text{-}6)$ $\Updownarrow$ $f(3)=\text{-}36$
$4$	$f(4)=6f(4-1)$ $\Updownarrow$ $f(4)=6f(3)$	$f(4)=6(\text{-}36)$ $\Updownarrow$ $f(4)=\text{-}216$
$5$	$f(5)=6f(5-1)$ $\Updownarrow$ $f(5)=6f(4)$	$f(5)=6(\text{-}216)$ $\Updownarrow$ $f(5)=\text{-}1296$
$6$	$f(6)=6f(6-1)$ $\Updownarrow$ $f(6)=6f(5)$	$f(6)=6(\text{-}1296)$ $\Updownarrow$ $f(6)\text{-}7776$
$7$	$f(7)=6f(7-1)$ $\Updownarrow$ $f(7)=6f(6)$	$f(7)=6(\text{-}7776)$ $\Updownarrow$ $f(7)=\text{-}46656$
$8$	$f(8)=6f(8-1)$ $\Updownarrow$ $f(8)=6f(7)$	$f(8)=6(\text{-}46656)$ $\Updownarrow$ $f(8)=\text{-}279936$
$9$	$f(9)=6f(9-1)$ $\Updownarrow$ $f(9)=6f(8)$	$f(9)=6(\text{-}279936)$ $\Updownarrow$ $f(9)=\text{-}1679616$
$10$	$f(10)=6f(10-1)$ $\Updownarrow$ $f(10)=6f(9)$	$f(10)=6(\text{-}1679616)$ $\Updownarrow$ $f(10)=\text{-}10077696$

Therefore, $f(2)=\text{-}6,$ $f(5)=\text{-}1296$ and $f(10)=\text{-}10077696.$