Chapter 12 Sequences and Series - 12.5 Use Recursive Rules with Sequences and Functions - 12.5 Exercises - Problem Solving - Page 832: 45

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Gladys owes $\$2000$ to a credit card company, $a_1=2000$ The company charges interest at a rate of 1.4% per month. The recursive rule for the balance of the account at the beginning of the nth month is $$a_n=1.014(a_{n-1}-100)$$ Obtain $a_{25}=1.014(a_{24}-100)=-76.6$ Hence, it will take 24 months to pay off the account.