Question

A pool pass costs $30 for the first month and $15 each additional month.

Construct an explicit rule in function notation to model the arithmetic sequence.
F(n) = ___________ (simplfy your answer)

Find F(12)

Answer 1

`F(n)=15(n+1)` [ where
`n` represents number of months]

`F(12)=195`

Explanation:

Pool pass cost for first month =$30

Pool pass cost after first month = $15 for each month

The total amount charged by the pool can be expressed as a function
`F(n)` where
`n` represents the number of months.

`F(n)=15(n-1)+30`

This can be simplified by using distribution.

`F(n)=(15n-15)+30`

`F(n)=15n-15+30`

`F(n)=15n+15`

Take 15 as greatest common factor.

∴
`F(n)=15(n+1)`

For
`n=12` months we plugin 12 for
`n` in the function.

`F(12)=15(12+1)`

`F(12)=15(13)`

`F(12)=195`

∴ Amount charged by pool for 12 months = $195