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, five cents on day 2, 25 cents on day three, and so on until the end of 16 days.
Part 1: Which choice should the lottery winner select?

Part 2: Using complete sentences, explain the procedure taken to answer this question.

Answer 1

i think you use geometric series :)

Answer 2

can you plug in the numbers into the formula?

Answer 3

the lump sum

Answer 4

ar^0+ar^1+ar^2+ar^3.... ar^15
day 1 2 3 4 .... 16
money .01 .05 .25 ... unknown
NOTE: in fact we dont even need to know what dayr 3 is. It just extra info.
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since r^0=1 (that is jsut a rule. Then a*1=a=.01
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Now we look at day 2
since r^1=r then
ar^1= ar thus pluging in and solving for r
.01*r=.05
r=.05/.01=5 r=5.
We almost there are you with me so far?

Answer 5

yes I think so

Answer 6

well we know
a=.01 aka always the first term
r=5
so we plug in the numbers. adding it all up

.01+.01*5+.01*5^2+.01*5^3 ... all the way to 15 but that will take forever.

thankfully there is a formula and it is.
http://www.purplemath.com/modules/series5.htm

Plugin in we get

.01*((1-5^15)/(1-5)) = 76293945.31

Answer 7

100,000,000
76,293,945.31

go with lump sum.

Answer 8

thank youu so much omg <3

Answer 9

LOL :D

Answer 10

save this page cuzz you will probably get more similar ones.

Answer 11

okay (: