Question

(30 points) HELP PLEASE
Also 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=\frac13(\text{current amount})=\frac13*450`

`a_2=\frac13a_1`

At the end of the third,
`a_3=\frac13(\text{new current amount})=\frac13a_2`

And so on. So the recursive rule is


`a_n=\frac13a_(n-1)`

starting with
`a_1=450`.