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Published byEthan Morgan Modified over 7 years ago
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 2+4+6+8+10… 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
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