A problem by Devery Sheridan

Level pending

If I go to an Automated Teller Machine (ATM), and I take out 1 dollar on the first day, 2 dollars on the second, and on each day I take out one more dollar than I did on the previous day, find how many dollars I will have taken out from the 350th day to the 2800th day, and add up all of the distinct prime factors of that number.


The answer is 77.

Devery Sheridan by Devery Sheridan , 23, USA

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1 solution

Devery Sheridan
Dec 22, 2013
  1. The problem assumes that each day one more dollar is taken out than was taken out on the previous day.
  2. To find the total number of dollars, we have to find an equation that sums all of this up. What we can do is find the average of the numbers and multiply it by the number of numbers.
  3. The number of numbers refers to the number of days.
  4. The average can be taken by only using the first and last numbers, and the equation we find for this is ((n1+n2)/2)
  5. The number of days can be found with the equation (n2-n1+1) for if we subtract 350 from 2800, we only include 351 to 2800, so a +1 must be added.
  6. By multiplying these two equations together, we get ((n1+n2)/2)(n2-n1+1).
  7. Plugging in, we get ((350+2800)/2)(2800-350+1)=3860250.
  8. The prime factors for this are 3, 3, 3, 5, 5, 7, 19, and 43
  9. The distinct prime factors for this are 3, 5, 7, 19, and 43.
  10. Adding these up, we get 77.
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