SOLUTION: I want to neqotiate an allowance with my parents propose that I make 1 cent the first week 2 cents the 2nd week 4 cents the 3rd week and 8 cents the 4th week, etc how much will I m

Algebra ->  Algebra  -> Sequences-and-series -> SOLUTION: I want to neqotiate an allowance with my parents propose that I make 1 cent the first week 2 cents the 2nd week 4 cents the 3rd week and 8 cents the 4th week, etc how much will I m      Log On

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Question 96045: I want to neqotiate an allowance with my parents propose that I make 1 cent the first week 2 cents the 2nd week 4 cents the 3rd week and 8 cents the 4th week, etc how much will I make after 52 weeks which happens to be total weeks for a year How much will I make the last week
Found 2 solutions by Earlsdon, edjones:
Answer by Earlsdon(6103) About Me  (Show Source):
You can put this solution on YOUR website!
This is a case of a geometrical progression and can be repesented as...
2%5E0%2B2%5E1%2B2%5E2%2B2%5E3%2B2%5E4+...+2%5E51%2B2%5E52
The sum of this progression is 2%5E52+-+1+=+4503599627370495cents
So, at the end of the year (52 weeks) you would have a total of:
$45,035,996,273,704.95
On the 52nd week, you would get:
2%5E%28%2852-1%29%29+=2251799813685248cents, which amounts to $22,517,998,136,852.48

Answer by edjones(7311) About Me  (Show Source):
You can put this solution on YOUR website!
1,2,4,8 is a geometric sequence.
the commmon ratio (r) is the ratio of one term to the term in front of it.
r=a%5B2%5D%2Fa%5B1%5D=2%2F1=2 in this case.
To find the nth term: a%5Bn%5D=a%5B1%5Dr%5E%28n-1%29
a%5B52%5D=1%2A2%5E%2851%29=2.2518%2A10%5E%2815%29=$225,180,000,000. for the last weeks pay check.
For the total 52 wks pay is the sum of the geometric series which is:a%5B1%5D%28%281-r%5En%29%2F%281-r%29%29
%281-2%5E52%29%2F%281-2%29=4.5036%2A10%5E%2815%29=$450,360,000,000.
EdJones