Study your flashcards anywhere!
Download the official Cram app for free >
 Shuffle
Toggle OnToggle Off
 Alphabetize
Toggle OnToggle Off
 Front First
Toggle OnToggle Off
 Both Sides
Toggle OnToggle Off
 Read
Toggle OnToggle Off
How to study your flashcards.
Right/Left arrow keys: Navigate between flashcards.right arrow keyleft arrow key
Up/Down arrow keys: Flip the card between the front and back.down keyup key
H key: Show hint (3rd side).h key
A key: Read text to speech.a key
38 Cards in this Set
 Front
 Back
converges

the infinite geometric series has a sum


diverges

the infinite geometric series has no sum


series

indicated sum of the terms of a sequence


arithmetic series

the sum of the terms in an arithmetic sequence


geometric series

the sum of the terms in a geometric sequence


geometric sequence

sequence in which the ratio of consecutive terms is a constant


common ratio

the constant in a geometric sequence ("r)


arithmetic sequence

sequence in which the difference between successive terms is a constant


arithmetic means

the average of two terms in an arithmetic sequence


geometric mean

the terms between two given terms in a geometric sequence


mean proportional

geometric mean


common difference

the constant in an arithmetic sequence


sequence

a function defined on the set of consecutive positive integers or a subset of consecutive positive integers


term

value in a sequence


general term

nth term


finite sequences

terminates


infinite sequence

never ends


recursive formula

ex: a1= 28
a(n+1)= (an) 4 (need past terms to solve) 

explicit formula

ex: a(n)=3(n)
(dont need past terms to solve) 

exponental equations

an equation with a variable in the exponent
ex: y= 3^x 

hyperbola

set of all points in a plane such that the difference of the distances from P to two fixed points is a constant


ellipse

set of all points in a plane such that the sum of the distances from P to two fixed points is a constant


parabola

set of all points P in a plane that are the same distance from a given line and a fixed point not on a line


circle

set of all points P in a plane that are the same distance (radius) from a given point (center)


rational algebraic function

function that can be represented as the quotient of two polynomials


asymptote

line (axis) the graph approaches but doesn't cross


location theorem

if f(x) is a polynomial function with real coefficients and a and b are real numbers such that f(a) is positive and f(b) is negative then at leaast one zero of f(x) occurs between a and b


upper bound

a number greater than or equal to the greatest real zero of the function


lower bound

a number less than or equal to the least zero of a function


complex conjugate theorem

if a complex number, a + bi, is a solution of a polynomial equation with real coefficients, then the conjugate, abi, is also a solution of the equation


rational zero theorem

if a polynomial function has integral coefficients and if it has a rational zero p/q where p and q are relatively prime, the p is a factor of the constant term and the q is a factor of the leading coefficient


remainder theorem

if p(x) is a polynomial and a is a number and if p(x) is divided by xa then the remainder is p(a)


factor theorem

if p(x) is a polynomial then xa is a factor of p(x) if and only if p(a)=0


complex number

sum of a real number and a pure imaginary number


radical equation

an equation that has a variable in the radicand


extraneous root

when you check it the answer does not work


perfect square

the product of two equal rational expressions


principal square root

the positive square root
