Answer:
Total membership for a year is $588
Total membership for 5 years is $60
Step-by-step explanation:
This is an arithmetic sequence of the form:
60, 58, 56, 54 ...
The first term is a = 60
the common difference is d = -2
We need to find the total member cost for a year, that is the sum of all the first 12 terms. We use the formula of sum of arithmetic sequence shown below:
[tex]S_n=\frac{n}{2}[2a+(n-1)d][/tex]
Where
a is first term
n is the number of term [here, 12]
d is common difference
From what we know, we can find:
[tex]S_n=\frac{n}{2}[2a+(n-1)d]\\S_{12}=\frac{12}{2}[2(60)+(12-1)(-2)]\\S_{12}=588[/tex]
Total membership for a year is $588
Now to find this for 5 years, we have to find 5*12 = 60 months.
So S_60, formula and find:
[tex]S_n=\frac{n}{2}[2a+(n-1)d]\\S_{60}=\frac{60}{2}[2(60)+(60-1)(-2)]\\S_{60}=60[/tex]
Total membership for 5 years is $60
