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You rent an apartment that costs $1500 per month during the first year, but the rent
is set to go up $140 per year. Write a recursive formula to show what the rent is
during the nth year of living in the apartment.
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Answer :

Answer:

[tex]\begin{cases}a_1 = 1500\\a_n = 140+a_{n-1}\end{cases}[/tex]

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Explanation:

[tex]a_1 = 1500[/tex] means the first term is 1500, ie this is the first rent value.

To get the next term, we add on $140

So

[tex]a_2 = 140+a_1 = 140+1500 = 1640[/tex]

and

[tex]a_3= 140+a_2= 140+1640 = 1780[/tex]

and so on.

In general, the nth term [tex]a_n[/tex] is found by adding 140 to the term just before it [tex]a_{n-1}[/tex]

So that's where [tex]a_n = 140+a_{n-1}[/tex] comes from.

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