Find the 288th term in the series ABBCCCDDDDEEEEEFFFFFF.........

1. 76

   rahul0324posted 11 years ago

   Find the 288th term in the series ABBCCCDDDDEEEEEFFFFFF.........
   
   A math question testing your series skill

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2. 78

   Aficionadaposted 11 years ago

   I haven't checked this yet, but I believe it is X.

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3. 56

   bubba-mathposted 11 years ago

   The position of the last occurrence of each letter is a triangular number. If the nth triangular number is x, it is given by x = n(n+1)/2. And so n in terms of x is given by the equation
   
   n = -0.5 + 0.5*sqrt(1+8x)
   
   Plugging x = 288 into the equation yields n = 23.5.  This means the 288th term is between the 23rd and 24th triangular numbers.  The 23rd letter is W and the 24th letter is X, so the 288th term is X.

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   1. 76

      rahul0324posted 11 years agoin reply to this

      You are very correct

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4. 0

   tigresosalposted 11 years ago

   The right answer will be W.
   Each alphabet here is repeated the number of times of its positional sequence in the series of alphabets. 1 A , 2 Bs, 3 Cs and so on. So we want to know where 288 comes as a result in the sequence 1+2+3+.......... and so on. 
   This sequence goes in an arithmetic progression with a sum characteristics with a formula x=n*(n+1)/2 or 288=n*(n+1)/2
   solving for n we get something that starts with 23 and ends with 24. W is a positional alphabet for 23 that will be start at a position 277 and will be repeated 23 times before the start of X that will start at a position of 301. So, the 288 th position will obviously be W and not X.

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   1. 76

      rahul0324posted 11 years agoin reply to this

      If you will solve in detail... you will come to find out it is X.... It is a CAT question and the answer was X.... try solving once more.... I did solve first with the natural progression method.,.. and then I sat to check it down... and I got X

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   2. 0

      tigresosalposted 11 years agoin reply to this

      Oh Yes! You are right. I missed the fact that W ends at 276 and thought that it would end at 300. Thanks a lot for correcting.

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   3. 76

      rahul0324posted 11 years agoin reply to this

      no worries friend... to err is human

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5. 69

   connorjposted 11 years ago

   After understanding the question, I can only conclude that X marks the spot...

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