 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.) 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 Please log in:
 Login: Password: Remember me: Sign up! | Forgot password

 Search: Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (4)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2019 by Animus Pactum Consulting. All rights reserved. Privacy Information