Question

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?

Answer 1

As you can see, the difference between two consecutive months is :
707.60-740=-32.4
and it is the same for third-second and fourth-third.
So we have indeed an arithmetic sequence where d=-32.4
Now, we have a1=740
so the general term of the sequence:
an = a1 + (n-1)d an = 740 + (n-1)*(-32.4)
an=772.4 -32.4n
an tells us how much money there is in the account in the nth month.
now we need to check when an=0 (the money is over)
772.4 = 32.4n n = 23.8
but this is not an integer and we are counting months so we will take 23 cause clearly for 24 we will have minus!
so n = 23. -> the account is good without depositing for 23 months (including the first)