Question

Which of the following graphs matches the pattern described above?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

an = a1 + (n - 1) * d
a1 = first term = 740
d = common difference = - 32.40
so ur arithmetic sequence can be modeled by :
an = 740 + (n - 1) * -32.40 or could also be written as : an = 740 - 32.40(n - 1)

how many months can u pay ur phone bill without depositing...
740/32.4 = 22.84......so it would be 23 months

lets check...sub in 23 for n
740 + (23 - 1) * -32.40
740 + 22(-32.40) =
740 - 712.80 =
27.2......correct, it would be 23 months....but u would still have $ 27.20 in ur account...not quite enough for another payment

Answer 2

Balance= 740 - 32.4m

Explanation:

The formula to represent the arithmetic formula is just the cost of each months phone bill, which is $32.4 this is multyplied by the number of months that you have to pay the bills and that is the total sum of the money that you have to pay, and you just have to withdraw the money from the total balance of the account, the number of months that you can pay with the $740 are 22.