Question

Paige borrows $700 from her parents for a new computer. She repays $100 the first month, and then begins to repay her parents $75 per month. Which recursive formula models the total amount of money still owed, mc022-1.jpg, at the end of the nth month?
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Answer 1

Let A_n be the amount owed at the end of month n. After 0 months A_0 = 700. She pays $100 in month 1, so A_1 = 600, and thereafter she pays $75 each month. Thus the recursive formula is

A_0 = 700, A_1 = 600,
A_n = A_{n-1} − 75 for n ≥ 2.

(Equivalently for n ≥ 1: A_n = 700 − 100 − 75(n−1) = 600 − 75(n−1).)