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

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rahul0324posted 8 years ago

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

A math question testing your series skill

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

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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.

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rahul0324posted 8 years agoin reply to this

You are very correct

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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.

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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

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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.

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rahul0324posted 8 years agoin reply to this

no worries friend... to err is human

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connorjposted 8 years ago

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

working