Lesson # ___ Section 9.1

A sequence is a function whose domain is the set of positive integers {1,2,3,4,5….} Sequences are listed in order so that there is a first member, a second member, a third member and so on.. You don’t have to write this down!

Ex. Kelly has $31 in her account and deposits $10 each week for the next 4 weeks. The # of dollars forms a sequence: 31, 41, 51, 61, 71 The numbers in a sequence are called TERMS a 1, a 2, a 3, a 4, …a n This is a finite sequence (it has a last term)

a 1, a 2, a 3, a 4, …a n a 1, a 2, a 3, a 4, … a n … This is a finite sequence (it has a last term) This is an infinite sequence (no last term)

Ex. Find the first 4 terms of the sequence given by a n = (-1) n 2n -1

Finding the n th term of a sequence Ex. Write an expression for the n th term (a n ) of each sequence. a. 1,3,5,7… #49.) 0, 3, 8, 15, 24… #53.) 1/2, -1/4, 1/8, -1/16,…

The Fibonacci Sequence is defined recursively a 0 = 1, a 1 = 1, a n = a n-2 + a n-1 1, 1, 2, ___, ___, ___, ___

Factorial Notation 6 ! = 6 * 5 * 4 * 3 * 2 * 1 n ! = n * (n-1) * (n-2) * … * 3 * 2 * 1 Note: 0 ! = 1 by definition

Summation (or Sigma) Notation See the definition on p 660 These are like algebraic adding machines. They produce a whole sequence of numbers and add them up.

And whatever you do, don’t forget to give lots of homework! I love this job! Try some examples! You need to write these on the board Mr. Bretsch. And don’t forget to mention the properties on p 661!