SOLUTION: what is the equation for this problem. A man has a job for thirty days, he will be paid 1 penny for the first day, 2 pennies for the second day, 4 pennies for the third day, and so

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Question 149502: what is the equation for this problem. A man has a job for thirty days, he will be paid 1 penny for the first day, 2 pennies for the second day, 4 pennies for the third day, and so on. What is the equation that would give the total amount of pennies for the 30th day?
this is not in the text book I have.
Found 3 solutions by stanbon, Nate, Edwin McCravy:
Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
The 30th day he will get 2^29 pennies.
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Cheers,
Stan H.
Answer by Nate(3500)   (Show Source): You can put this solution on YOUR website!
This is actually a geometric sum or series.
S = a1(1 - r^n)/(1 - r)
S: sum, a1: first term, r: rate, n: # of terms
A man has a job for thirty days, he will be paid 1 penny for the first day, 2 pennies for the second day, 4 pennies for the third day, and so on. What is the equation that would give the total amount of pennies for the 30th day?
1 + 2 + 4 + 8 + ... a1 * r^(n - 1) or 2^(n - 1)
a1 = 1, r = 2, n = 30
S = (1 - 2^30)/(1 - 2) = 1,073,741,823 pennies or $10,737,418.23
Answer by Edwin McCravy(20060)   (Show Source): You can put this solution on YOUR website!

what is the equation for this problem. A man has a job for thirty days, he will be paid 1 penny for the first day, 2 pennies for the second day, 4 pennies for the third day, and so on. What is the equation that would give the total amount of pennies for the 30th day?
this is not in the text book I have. 

I can't tell whether you want to know the number of pennies received
on just the 30th day only, or whether you want the total number of 
pennies received in all the 30 days.

If you want to know just how many pennies he received on the 30th day
only:

The nth term of a geometric series  is given by



where 
,
 


Substituting,



This is how many pennies ge would receive of the 30th day
ONLY, well over 5 million dollars!

----------------------------

If you want to know how many pennies he would receive in all 30
days total, the sum of the first n terms of a geometric 
series  is given by



where 
,
 


Substituting,



well over 10 million dollars!

Edwin
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