Suppose your business has a special checking account used just for paying the phone bill. The balance is $740.00 this month. Next month the balance will be $707.60, after that it will be $675.20, and on the third month the balance will be $642.80. Write an explicit formula to represent the balance in the account as an arithmetic sequence. How many months can you pay your phone bill without depositing any more money in the account?

740 - 707.6 = 32.4

707.6 - 675.20 = 32.4

675.20 - 642.8 = 32.4

Balance = 740.0 - 32.4 (n-1), where n - 1 is the humber of months elapsed.

The second question may be answered by finding when the sum of the terms equal the original amount in the account.

This is: Sum of S1 + S2 + S3 + ... = 740.0

Now you can either use the equation that gives the sum of terms of an arithmetic progression - which is Sn = [A1 + An]*n/2, where A1 is the first term and An is the nth term, or going down 32.40 step-by-step.

The result is that at month 23 the account will have 27.20, then you have to deposit to pay the next months.