Question

A dream club charges $60 for the first month of membership, and $2 less each month after that. (Yes, after a while the dream club starts paying money to members instead of charging them :)). What is the total membership for a year? For 5 years?

Answer 1

Total membership for a year is $588

Total membership for 5 years is $60

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:

`S_n=(n)/(2)[2a+(n-1)d]`

Where

a is first term

n is the number of term [here, 12]

d is common difference

From what we know, we can find:

`S_n=(n)/(2)[2a+(n-1)d]\\S_(12)=(12)/(2)[2(60)+(12-1)(-2)]\\S_(12)=588`

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:

`S_n=(n)/(2)[2a+(n-1)d]\\S_(60)=(60)/(2)[2(60)+(60-1)(-2)]\\S_(60)=60`

Total membership for 5 years is $60