By Sheldon, Megan, Jimmy, and Grant.. Sequence- list of numbers that usually form a pattern. Each...
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Transcript of By Sheldon, Megan, Jimmy, and Grant.. Sequence- list of numbers that usually form a pattern. Each...
CHAPTER 9A AN INTRO TO SEQUENCES
By Sheldon, Megan, Jimmy, and Grant.
9.1A
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……
9.1A
General rule an=2n where n is the # and an is the nth
term
The general rule can also be written in function notation: F(n)=2n
9.1A
Recursive sequence Must give you a1 or a1 and a2
Must give a rule for finding terms based on previous terms.
Example: Ak+1 = (-2)ak
9.1B
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
9.1B
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
5
1
2i
9.1B
Summation notation for an infinite series
Example 2+4+6+8+10… would be
1
2i
9.2
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 An=a1+(n-1)d
9.2
Sum of finite Arithmetic Sequence Sn=n/2 (a1 + an) Example:
2,8,14,20…n=25 S25= 25/2 (2+146) a25=2+(25-1)
(6) S25= 1850 a25= 146
9.3
Geometric Sequences Ratios of consecutive terms are the same
Example: (a2/a1)= r, a3/a2=r, a4/a3=r
To find the nth term of a geometric sequence you use (an)=a1r^(n-1)
9.3
To find the Sum of a Finite Geometric Sequence you use the formula
n
i
nir
r
raa
1
^1)1(^11
1
9.4
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 an=an+b
If all the 1st differences are different, but the 2nd differences are equal, the sequence has a quadratic model an=an^2+bn+c