Sequences are functions which takes natural number and turns into different value. Sequences have a domain of natural numbers. Define sequences with recursive definition or closed form definition.
Recursive Definition:
U1 = 3
Un = 2 * U n-1
Closed Form Definition:
Example with 1, 1, 2, 3, 5, 8, 13...
U1 = 1
U2 = 1
Un = Un-1 + Un-2
Another example:
Write first five terms.
U1 = 5
Uk+1 = Uk +3
5, 8, 11, 14, 17
A series a set of numbers from sequences and added together.
Example: If the set was {4, 9, 16, 25, 36, 49} then 4 + 9 + 16 + 25 +36 + 49 = x
Sigma notation shows us the limits of the set.
SIGMA =
lower limit goes underneath the sigma and is usually positive integer. Example i=1. Upper limit goes above the sigma and is larger than the lower limit. Example:
(1+1)2 + (2+1)2 + (3+1)2 + .... + (6+1)2
Stop at six because six is upper limit.
At the end of class we worked on using our calculators to help us with sequence mode. Guides how to do that and the homework is posted below for the next class. The next scribe is Keegan.
And Mr. O'Brien, where can I find your iCal link?
The iCal link is on the class website under red 3.
ReplyDeleteThanks, Robin!
ReplyDeleteNice entry, Maci. I think your Closed Form examples are actually Recursive, though. Closed Form will be a formula in terms of n, not in terms of previous term(s).