Question

A lottery winner must decide between two methods of payment. Choice one is to receive a lump sum of $100,000,000. Choice two is to begin with one cent on day 1, four cents on day 2, 16 cents on day three, and so on until the end of 18 days. Which choice should the lottery winner select? Using complete sentences, explain the procedure taken to answer this question.

Answer 1

@redshift, it's part of the arithmetic and geometric sequences

Answer 2

Method 1: Total amount of money: $100 000 000.00

Method 2:

Notice that the number of cents earned each day is according to 4^n where n represents the day. So for 18 days the number of cents would be 4^17(Since 2^0 is day 1). This equals 68719476736 cents.

Divide by 100 to convert this to dollars. 68719476736/100 = $687 194 767.36

So method 2 gives $687 194 767.36 which is much greater than $100 000 000. I would take the second method of payment for sure :)

Answer 3

Oh okay, thanks. I thought I got that question wrong, now I realize just how wrong it was lol. Thanks for the help!

Answer 4

Np :)

Just note that "So for 18 days the number of cents would be 4^17(Since 2^0 is day 1)."

should say, "So for 18 days the number of cents would be 4^17(Since 4^0 is day 1)."

Answer 5

I thought I had to use the geometric sequence formula for this.

Answer 6

You could use that formula. Because it is a geometric sequence.

Answer 7

Can you show me the process with the geometric sequence formula?

Answer 8

Do you normally use the x(n) = a*r^(n-1) formula?

Answer 9

Yes.

Answer 10

Ok.

Using that notation:
x(n) - the nth term in the sequence
a - the first term (in our case: 1[cent])
r - the common ratio (we can tell that it is 4 because we see that the second term is 4)

So the formula as a geometric sequence is:
x(n) = 1*4^(n-1)
or x(n) = 4^(n-1)

solving for the 18th day:
x(18) = 4^(18-1)
x(18) = 4^17
x(18) = 68719476736

which you then convert to cents...

Answer 11

Oh okay, got it. I used the sn=a1-a1r^n/1-r formula for this. Thanks! :)