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

Answer:

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

$F(12)=195$

Step-by-step 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