Question

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 1

`\begin{cases}a_1 = 1500\\a_n = 140+a_(n-1)\end{cases}`

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Step-by-step explanation:

`a_1 = 1500` means the first term is 1500, ie this is the first rent value.

To get the next term, we add on $140

So

`a_2 = 140+a_1 = 140+1500 = 1640`

and

`a_3= 140+a_2= 140+1640 = 1780`

and so on.

In general, the nth term
`a_n` is found by adding 140 to the term just before it
`a_(n-1)`

So that's where
`a_n = 140+a_(n-1)` comes from.