 All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars  perplexus dot info  Difficult Sequence (Posted on 2003-10-18) 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) Comments: ( Back to comment list | You must be logged in to post comments.) 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 Please log in:
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