Question

GEOMETRIC SERIES/SEQUENCE: 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, three cents on day 2, nine cents on day three, and so on until the end of 22 days.

Which choice should the lottery winner select?

How would I solve it using the formulas for series and sequences?

Answer 1

lmao @WeedKushh_

Answer 2

Day=n
a(n)=∑1223n−1
This gives you a value in cents, which you then have to find by dividing by 100 because:
a(n)∗$1100¢=$$$
And how in the blazes did I get that general formula? By writing the first few terms (would be nice if there was more to be certain it's not something fancy & complicated but hey) Day 1, 1¢ Day 2, 3¢ Day 3, 9¢ This looks a lot like a 3^x exponential to me, but if n starts with 1, we have to subtract 1 so that 3^0 = 1
a(1)=3(1)−1=30=1¢
a(2)=3(2)−1=31=3¢
a(3)=3(3)−1=32=9¢
a(4)=3(4)−1=33=27¢
a(5)=3(5)−1=34=81¢
a(6)=3(6)−1=35=$2.41
yeah it grows exponentially until
a(22)=3(22)−1=321=$104,603,532

Id go with second choice lol.

Answer 3

http://openstudy.com/study#/updates/4fc2a574e4b0964abc83ee5d

Answer 4

@icetea still need help? do you understand geometric sequences?

Answer 5

Describe a real world scenario that is an arithmetic series. Show your work as you find the 7th term of your scenario. @agent0smith could i just use money as an example?

Answer 6

or would that be geometric not arithmtic?

Answer 7

hmm, money in what way? As in coins like 1c, 5c, 10c, 25c, $1?

Answer 8

yeah i just need to make it an arithmetic series

Answer 9

You could use this example:

http://wiki.answers.com/Q/How_do_you_use_arithmetic_sequences_in_real_life

A theater has 60 seats in the first row, 68 seats in the second row, 76 seats in the third row, and so on in the same increasing pattern.

Then find the 7th term (seventh row of seats)

Answer 10

which formula would i use ?

Answer 11

an=a1+(n-1)d

Answer 12

Correct. n is 7 for the 7th term. Can you find a1 and d?

Answer 13

60=a1, and d=8

Answer 14

Good, now find a7 using the formula.

Answer 15

108? are you sure this is for series not sequence

Answer 16

a7 = 60 + (7-1)*8 = 108 :)

Well a series means you're adding the terms of a sequence, but you're only asked to find term 7 so you're fine.

Answer 17

Oh alright thanks!!

Answer 18

np. The series would just be the rows of the theater added together... 60+68+76+...

Answer 19

http://www.purplemath.com/modules/series4.htm

"An arithmetic series is the sum of an arithmetic sequence. A geometric series is the sum of a geometric sequence. "

Answer 20

Thanks!

Answer 21

:)