SOLUTION: Please help me to figure out this word problem. Thank you. Suppose an employee recieves a wage of 1 cent for the first day of work, 2 cents the second day, 4 cents the third day

Algebra ->  Algebra  -> Sequences-and-series -> SOLUTION: Please help me to figure out this word problem. Thank you. Suppose an employee recieves a wage of 1 cent for the first day of work, 2 cents the second day, 4 cents the third day      Log On

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Question 84882: Please help me to figure out this word problem. Thank you.
Suppose an employee recieves a wage of 1 cent for the first day of work, 2 cents the second day, 4 cents the third day, and so on in a geometric sequence. Find the total amount of money earned for working 30 days.
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
A sequence of numbers each of which is progressively increased by the same factor, in this case, the factor is 2, is known as a geometric progression.
2%5E0%2B2%5E1%2B2%5E2%2B2%5E3%2B2%5E4+...+2%5E%28n-1%29%2B2%5En
It can be shown that the sum of all the terms in such a progression is given by:
S+=+2%5En+-+1
In your problem, n = 30 (the number of days), so, the total number of cents (S) received for 30-days work would be:
S+=+2%5E30+-+1
S+=+1073741824+-+1
S+=+1073741823 cents. Multiply by 100 to find the number of dollars.
S+=+10737418.23
The employee receives $10,737,418.23 for 30-days work.