Question

Mark must pay a $250 non-refundable pet deposit for his apartment. If rent is $850 per month , then write a expression that would model his rent over time ! Explain how this relates to the airthmetic sequence we have been studying .

Answer 1

The expression to model Mark's rent over time is R(n) = 850n + 250. It's an arithmetic sequence where the monthly rent is the common difference and the initial deposit is the first term.

Step-by-step explanation:

Mark's rent over time can be modeled as an arithmetic sequence because he pays a consistent amount each month, with a one-time pet deposit. The arithmetic sequence for rent payment would be the sequence of his monthly rent plus the initial pet deposit. So, if we let n represent the number of months that Mark has rented the apartment, the total amount paid after n months would be given by the expression:

R(n) = 850n + 250
Here, 850n represents the rent paid each month, and 250 represents the one-time non-refundable pet deposit. This relates to the arithmetic sequence we have been studying because in any arithmetic sequence, each term after the first is found by adding a constant, called the common difference, to the previous term. In this case, the common difference is the stable monthly rent of $850, and the initial term is $250, the initial deposit.