By Sheldon, Megan, Jimmy, and Grant.

 Sequence- list of numbers that usually form a pattern.  Each number in the list is called a term.  Finite sequence 2,4,6,8  Infinite sequence 2,4,6,8……

 General rule  a n= 2n where n is the # and a n is the nth term  The general rule can also be written in function notation: F(n)=2n

 Recursive sequence  Must give you a 1 or a 1 and a 2  Must give a rule for finding terms based on previous terms.  Example:  A k+1 = (-2)a k

 Factorial  If n is a positive integer, then n!=n(n-1)(n-2)…  Example:  4! 4(3)(2)(1)= 24  Series  The sum of the terms in a sequence  Can be finite or infinite

 Summation Notation  Also called sigma notation(meaning Sum ∑ in Greek)  Example:  (i) is called the index of summation  5 is called the upper limit  1 is called lower limit

 Summation notation for an infinite series  Example  … would be

 Arithmetic Sequence  Has a common difference between consecutive terms  That’s the number you add to each term to get the next term  Subtract any term by its previous  Rule for arithmetic sequence  A n =a 1 +(n-1)d

 Sum of finite Arithmetic Sequence  S n =n/2 (a 1 + a n )  Example:  2,8,14,20…n=25  S 25 = 25/2 (2+146) a 25 =2+(25-1)(6)  S 25 = 1850 a 25 = 146

 Geometric Sequences  Ratios of consecutive terms are the same  Example:  (a 2 /a 1 )= r, a 3 /a 2 =r, a 4 /a 3 =r  To find the nth term of a geometric sequence you use  (a n )=a 1 r^( n - 1 )

 To find the Sum of a Finite Geometric Sequence you use the formula

 Mathematical Induction  A mathematical proof about statements involving positive integers  Finite Difference  If all the first difference in the sequence are equal, then the sequence has a linear model a n =an+b  If all the 1 st differences are different, but the 2 nd differences are equal, the sequence has a quadratic model a n =an^ 2 +bn+c