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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)

Comments: ( Back to comment list | You must be logged in to post comments.)
re: An alternate approach - I think I got it | Comment 16 of 19 |
(In reply to An alternate approach by Brian Smith)

The nth term can be expressed as a function by finding the formulas for the two subsequences.
f(n) for odd n = (1/2)*n^2 + (41/2)*n
f(n) for even n = (3/2)*n^2 + (39/2)*n

These two sequences can be combined, utilizing (-1)^n:
f(n) = n^2 + 20*n + ((-1)^n)*((1/2)*n^2-(1/2)*n)

In other words, to calculate the nth term find n^2 + 20*n and the (n-1)th triangular number. If n is even then take the sum and if n is odd then take the difference.
  Posted by Brian Smith on 2003-10-27 10:46:37

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