You rent an apartment that costs $1800 per month during the first year, but the rent is set to go up 9.5% per year. Write a recursive formula to show what the rent is during the nth year of living in the apartment.

Step-by-step explanation:

You rent an apartment that costs \$1800$1800 per month during the first year, but the rent is set to go up \$160$160 per year. What would be the monthly rent during the 9th year of living in the apartment?

\text{Write out the first 3 terms:}

Write out the first 3 terms:

a_1=1800\leftarrow \text{rent in 1st year}

a

1

=1800←rent in 1st year

a_2=1960\leftarrow \text{rent in 2nd year}

a

2

=1960←rent in 2nd year

a_3=2120\leftarrow \text{rent in 3rd year}

a

3

=2120←rent in 3rd year

\text{Arithmetic Sequence: }d=160

Arithmetic Sequence: d=160

The common difference

\text{Explicit Formula: }

Explicit Formula:

a_n=

a

n

=

\,\,a_1+(n-1)d

a

1

+(n−1)d

a_{\color{green}{9}}=

a

9

=

\,\,1800+(\color{green}{9}-1)(160)

1800+(9−1)(160)

a_{9}=

a

9

=

\,\,3080

3080