The car has at the begining of the lease.

The number of additional miles must be less than .

(a) Find the sequence for the maximum number of allowed miles.

The sequence by adding to the previous term.

.

.

.

Therefore, the sequence is .

(b) Find the first four terms of the sequence.

In the first month, the customer pays the down payment plus the first month lease payment.

After that, the customer pays just the lease payment each month.

The down payment is and first month lease payment is .

.

.

.

.

Therefore,the first four terms of the sequence are .

(c) Find the explicit formula to represent the sequence in part (b).

The sequence is .

Observe the sequence in part (b):

Each term an in this sequence can be found by adding multiple number of to an initial value of .

So an explicit formula for this sequence is an .

(d) Find the total money pain by the end of the lease.

The time period of the lease is .

Find the value of .

The explicit sequence is .

Substitute .

The total amount of money paid by the end of the lease is .

(a) The sequence is .

(b)  The first four terms of the sequence are .

(c) An explicit formula for this sequence is an .

(d)  The total amount of money paid by the end of the lease is .