Question
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.(1 point)
an=an−1+
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.(1 point)
an=an−1+
Answers
GPT-4o mini
To write a recursive formula for the rent in the nth year of living in the apartment, we can define the sequence as follows:
- Let \( a_n \) be the rent in the nth year.
- The rent in the first year, which is the base case, is \( a_1 = 1700 \).
- The rent increases by $70 each subsequent year, so the recursive relationship can be expressed as:
\[
a_n = a_{n-1} + 70
\]
for \( n > 1 \).
So, the complete recursive formula is:
\[
\begin{align*}
a_1 & = 1700 \\
a_n & = a_{n-1} + 70 \quad \text{for } n > 1
\end{align*}
\]
- Let \( a_n \) be the rent in the nth year.
- The rent in the first year, which is the base case, is \( a_1 = 1700 \).
- The rent increases by $70 each subsequent year, so the recursive relationship can be expressed as:
\[
a_n = a_{n-1} + 70
\]
for \( n > 1 \).
So, the complete recursive formula is:
\[
\begin{align*}
a_1 & = 1700 \\
a_n & = a_{n-1} + 70 \quad \text{for } n > 1
\end{align*}
\]