TEXTBOOK: $10\mathrm{.}1$

A ball $is$ thrown upward $to$ a height $of{h}_0$ meters. After each bounce, the ball rebounds $toa$

fraction $rof$ its previous height. Let $h_{n}be$ the height after the $nth$ bounce and let $S_{n}be$ the total

distance the ball has traveled $at$ the moment $of$ the $nth$ bounce.

Suppose a racket ball bounces with $h_0=10$ and $r=0\mathrm{.}82.$

$a.$ Find the first four terms $of$ the sequence $\{h_n\}.$

$b.$ Find a recurrence relation for the sequence $\{h_n\}.$

$c.$ Find $an$ explicit formula for the sequence $\{h_n\}.$

$d.$ What $is$ the $limitof$ the sequence $\{h_n\}?e.$ Find the first four terms $of$ the sequence $\{S_n\}.$

$f.$ Find a recurrence relation for the sequence $\{S_n\}.$

$g.$ Find $an$ explicit formula for the sequence $\{S_n\}.$ Hint: You will need a sigma.

$h.$ What $is$ the $limitof\{S_n\}?$

$In$ the long run, how far will the ball travel? Justif$\frac{y}{e}$xplain how you arrived $at$ your answer.