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Difficult Sequence (Posted on 2003-10-18) Difficulty: 5 of 5
What is the next number in the sequence? 21,45,66,102,115,171,?

See The Solution Submitted by Freddy Grants    
Rating: 3.6667 (9 votes)

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Solution Problem Solution Comment 19 of 19 |

Define S(n) = (20 + 21+ .......+(19+n))
and, U(n) = (20 + 19+ .......+ (21-n))
Then, the  terms of the sequence T(n) is:
T(n)
= n^2 + S(n), where n is even
= n^2 + U(n), where n is odd

For example, T(2) would be 2^2+ 20+21 = 45, while T(3) would be 3^2+ 20+19+18 = 66

Consequently, the missing term is:
T(7)
= (20 + 19+...+14) + 7^2
= 119 + 49
= 168


 


  Posted by K Sengupta on 2007-04-20 14:57:03
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