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31 Cards in this Set
- Front
- Back
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An _________ ________ is a function whose domain is the set of positive integers
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Infinite Sequence
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A ______ ________ is one which contains only the first n positive integers. It ends. Its terms can be counted.
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Finite Sequence
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A _________ _______ is one that relies on the values of previous terms
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Recursive Sequence
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A ______ is the sum of the terms of a sequence
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Series
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An ________ ________ is the sum of all the terms of an infinite sequence.
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Infinite Series
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A ______ ________ is the sum of the first n terms of a sequence
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Finite Series
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The sum of the first n terms of a finite sequence is also referred to as the ___ _______ ___
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nth partial sum
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The sum of the first n terms of a sequence is called? and is represented by?
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Series Summation Notation (aka Sigma Notation)
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A sequence is _________ if the difference between consecutive terms is a constant
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Arithmetic
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The recursive formula for an arithmetic sequence with a common difference d is ____________ and what must be specified?
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a n+1 = a n + d. a1 must be specified
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what is the nth term formula for an arithmetic sequence with a common difference?
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an = a1+(n-1)d
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A sequence is _________ if the ratio between consecutive terms is a constant
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geometric
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The recursive formula for a geometric sequence is what?
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a n+1=an*r
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the nth term formula for a geometric sequence is what?
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an=a1r^n-1
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What is the sum formula for a finite arithmetic sequence
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Sn=[(n/2)*(a1+an)}
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What is the sum formula for a infinite geometric sequence?
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S= (a1)/(1-r)
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What is the Compounding Interest Formula?
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A=P[1+(r/n)]^m
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What is the formula for the finite geometric sequence?
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Sn=a1*[(1-r^n)/(1-r)]
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How do you find the x intercept
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set Y to be 0 and solve
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How do you find the y intercept
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set X to be 0 and solve
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Graphs with ______ symmetry are NOT functions
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x-axis
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Explain Origin symmetry
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when x,y is on the graph and -x, -y is on the graph
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Explain the 3 Algebraic Tests for Symmetry
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1. The graph of an equation has x-axis symmetry if replacing y with (-y) yields an equivalent equation. 2. The graph of an equation has y-axis symmetry if replacing x with (-x) yields an equivalent equation. 3. The graph of an equation has origin symmetry if replacing x with (-x) and y with (-y) yields an equivalent equation
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Explain explicit relation
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If an equation is solved for y in terms of only x and constants, than it is an explicit relation.
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Explain an implicit function
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When the relation is not solved for y`
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What is a set
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collection of objects
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What is a relation
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A correspondence between two sets
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If the domain is not specified, the _______ ______ consists of all real numbers
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implied domain
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What is the difference quotient?
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Gives the slope of the secant line passing through the points (x, f(x)) and (x+h, f(x+h). It is often used to approximate the slope of the tangent line
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What is an even function
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if f(-x)=f(x)
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what is an odd function
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if f(-x)=-f(x)
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