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Website losing interest


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Question

My friend's music fan website started out fast: lots of visitors the first week. But every week, there were fewer and fewer; the second week there was one more visitor than 2/3 of the first week, the 3rd week there were 2 more than 2/3 of the second week, the 4th week there were 3 more than 2/3 of the 3rd week, and so on, until the final week, when there were just 533.
How many weeks was the website up?
How many visitors did it get the 1st week?
How many total visitors were there?
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Not sure if this is the only solution.

1st week: 19677 visitors

2nd week: 19677*2/3+1=13119

3rd week: 13119*2/3+2=8748

4th week: 8748*2/3+3=5835

5th week: 5835*2/3+4=3894

6th week: 3894*2/3+5=2601

7th week: 2601*2/3+6=1740

8th week: 1740*2/3+7=1167

9th week: 1167*2/3+8=786

10th week: 786*2/3+9=533

Total visitors: 19677+13119+8748+5835+3894+2601+1740+1167+786+533=58100

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