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

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  1. rahul0324 profile image81
    rahul0324posted 8 years ago

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

    A math question testing your series skill smile

  2. Aficionada profile image88
    Aficionadaposted 8 years ago

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

  3. bubba-math profile image59
    bubba-mathposted 8 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.

    1. rahul0324 profile image81
      rahul0324posted 8 years agoin reply to this

      You are very correct smile

  4. profile image0
    tigresosalposted 8 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.

    1. rahul0324 profile image81
      rahul0324posted 8 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

    2. profile image0
      tigresosalposted 8 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.

    3. rahul0324 profile image81
      rahul0324posted 8 years agoin reply to this

      no worries friend... to err is human smile

  5. connorj profile image75
    connorjposted 8 years ago

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


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