Question

You rent an apartment that costs $1700$1700 per month during the first year, but the rent is set to go up $70$70 per year. Write a recursive formula to show what the rent is during the nth year of living in the apartment.

Answer 1

To represent the rent during the \( n \)th year of living in the apartment using a recursive formula, we can define the following:

Let \( R(n) \) be the rent during the \( n \)th year.

1. For the first year (\( n = 1 \)), the rent is $1700:
\[
R(1) = 1700
\]

2. For each subsequent year (from the second year onwards), the rent increases by $70 per year. Thus, the recursive relation can be expressed as:
\[
R(n) = R(n-1) + 70 \quad \text{for } n > 1
\]

Putting it all together, the recursive formula for the rent \( R(n) \) during the \( n \)th year is:

\[
R(1) = 1700
\]
\[
R(n) = R(n-1) + 70 \quad \text{for } n > 1
\]

This formula allows you to calculate the rent for any year \( n \) based on the previous year's rent.