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### 38 Cards in this Set

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 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 n-th 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, a-bi, 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 x-a then the remainder is p(a) factor theorem if p(x) is a polynomial then x-a 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