Exercise $($a$)$

Find the first five terms of the sequence $\{$a$\_($n$)\}.$

Step $1$

For a$\_($n$)=8000(1\mathrm{.}02)^($n$),$ we have a$\_(1)=8000(1\mathrm{.}02)^(1)=8160$

and a$\_(2)=8000(1\mathrm{.}02)^(2)=8323\mathrm{.}2$

$8323\mathrm{.}20$

Step $2$

Rounding answers to two decimal places, we similarly have a$\_(3)=8489\mathrm{.}66,8489\mathrm{.}66,$a$\_(4)=8659\mathrm{.}46,8659\mathrm{.}46,$a$\_(5)=8832\mathrm{.}64,8832\mathrm{.}65.$

Exercise $($b$)$

Is the sequence convergent or divergent?

Stop $1$

Since $1\mathrm{.}02$ is greater than $1,$ we have the following. $($If an answer does not exist, enter DNE.$)\backslash$lim$\_($n$->\backslash$infty $)(1\mathrm{.}02)^($n$)=$

SKIP $($YOU CANNOT COME BACK$)$