TAILIEUCHUNG - Mathematics - Lecture 20: Arithmetic and geometric sequences

Mathematics - Lecture 20 provides knowledge of arithmetic and geometric sequences. The main contents of the chapter consist of the following: Sequences, arithmetic sequences, geometric sequences. | Arithmetic and Geometric Sequences Mathematics 17 Institute of Mathematics, University of the Philippines-Diliman Lecture 20 Math 17 (UP-IMath) Arithmetic and Geometric Sequences Lec. 20 1 / 23 Outline 1 Sequences 2 Arithmetic Sequences 3 Geometric Sequences Math 17 (UP-IMath) Arithmetic and Geometric Sequences Lec. 20 2 / 23 Sequences Definition A sequence is an ordered set of numbers. The numbers in the sequence are called terms. Math 17 (UP-IMath) Arithmetic and Geometric Sequences Lec. 20 3 / 23 Sequences Definition A sequence is an ordered set of numbers. The numbers in the sequence are called terms. Examples: 1 2, 4, 6, 8, 10, 12, . . . 2 2, 3, 5, 7, 11, 13, . . . 3 20, −10, 5, − 5 , 5 , − 5 , . . . 2 4 8 4 4, 2, 8, 6, 12, 10, . . . Math 17 (UP-IMath) Arithmetic and Geometric Sequences Lec. 20 3 / 23 Sequences Definition A sequence is an ordered set of numbers. The numbers in the sequence are called terms. Examples: 1 2, 4, 6, 8, 10, 12, . . . 2 2, 3, 5, 7, 11, 13, . . . 3 20, −10, 5, − 5 , 5 , − 5 , . . . 2 4 8 4 4, 2, 8, 6, 12, 10, . . . The last sequence is different from the first sequence though the same numbers appear in the sequences. Math 17 (UP-IMath) Arithmetic and Geometric Sequences Lec. 20 3 / .

• Toán học
• Lecture Mathematics
• Geometric sequences
• Arithmetic sequences
• Axioms on equality
• Cancellation laws
• Real number line
• Lecture Business mathematics
• Bài giảng Toán kinh doanh
• Business mathematics
• Financial mathematics
• Net present value
• Internal rate of return
• Mathematics 53
• Lecture Mathematics 53
• Integrals yielding logarithmic
• Exponential functions
• Integrals of exponential functions
• Natural logarithmic function
• Inverse circular functions
• Integrals yielding
• Derivatives of inverse circular functions
• Graphs of inverse circular functions
• Hyperbolic functions
• Inverse hyperbolic functions
• Derivatives of hyperbolic functions
• Indeterminate forms
• L’Hôpital’s rule
• Polynomial functions
• Basic types of functions
• Constant functions
• Linear functions
• Limit of a function
• One sided limits
• Limit theorems
• One sided limit
• Infinite limits
• The greatest integer function
• Vertical asymptotes
• Infinity formal definition
• Intuitive definition
• Horizontal asymptotes
• Continuity of functions
• Continuity on an interval
• Essential discontinuity
• The intermediate value theorem
• The squeeze theorem
• Trigonometric functions
• Continuity of trigonometric functions
• Differentiation rules
• The tangent line
• Definition of the derivative
• The chain rule
• Chain rule theorem
• Funtion theorem
• Geometric interpretation of differentiability
• Higher order derivatives
• Implicit differentiation
• Local linear approximation
• Rates of change
• Rectilinear motion
• Position function
• Instantaneous velocity
• Related rates
• Function of time
• Problem on related rates
• Numerical facts
• Mean value theorem
• Relative extrema
• Critical numbers
• Decreasing functions
• The second derivative test
• Points of inflection
• Graphing polynomials
• Second derivative
• Graphing functions
• Vertical asymptotes
• Oblique asymptotes
• Absolute extrema
• Bounded intervals
• One relative extremum
• Absolute maximum
• Optimization word problems
• Optimization problems
• Solving optimization problems
• Integration by substitution
• Theorems on antidifferentiation
• Substitution rule
• Particular antiderivatives
• Application to rectilinear motion
• Plane region
• The definite integral
• Properties of the definite integral
• General antiderivative
• The second fundamental theorem of calculus
• Arc length
• Area of a plane region
• Horizontal rectangles