Question

(30 points) HELP PLEASEAlso include how you did it please. I need to know how to solve this.

Answer 1

Let $a_n$ be the amount of money he has in the account at the end of the $n$th month.

So at the end of the first month (assuming he doesn't make a withdrawal then) he would have

$a_1=450$.
 
Halfway through the next month, he withdraws 1/3 of the account. The account doesn't earn interest, so only his withdrawals affect the amount of money in the bank. So at the end of the second month, he would have

$a_2=\dfrac13(\text{current amount})=\dfrac13\times450$
$a_2=\dfrac13a_1$

At the end of the third, $a_3=\dfrac13(\text{new current amount})=\dfrac13a_2$

And so on. So the recursive rule is

$a_n=\dfrac13a_{n-1}$

starting with $a_1=450$.