![]() Next two terms are \(,\,\,\_\_\,\,\,\_\_\) On the top (numerator), the next term is 1 more than the previous one, and the bottom (denominator), the next term is the previous term multiplied by 2. For example, try to find the next few terms in the following sequences:ġ, 8, 27, _, _ Every term is cubed. You may have heard the term inductive reasoning, which is reasoning based on patterns, say from a sequence (as opposed to deductive reasoning, which is reasoning from rules or definitions). Sequences are the list of these items, separated by commas, and series are the sum of the terms of a sequence (if that sum makes sense it wouldn’t make sense for months of the year). Each of these numbers or expressions are called a term or an elements of the sequence. Sequences are basically just numbers or expressions in a row that make up some sort of a pattern for example, January, February, March, …, December is a sequence that represents the months of a year. Note that Limits of Sequences are discussed here in the Limits and Continuity section. Introduction to Sequences and Series Arithmetic Series Summary of Formulas for Sequences and Series Summation Notation Sequences and Series Definitions Geometric Series Explicit Formulas Versus Recursive Formulas Finite Geometric Series Arithmetic Sequences Infinite Geometric Series Geometric Sequences Applications of Sequences and Series Writing Formulas Sequences and Sums on the Graphing Calculator More Practice Applications of Integration: Area and Volume.Exponential and Logarithmic Integration.Riemann Sums and Area by Limit Definition.Differential Equations and Slope Fields.Antiderivatives and Indefinite Integration, including Trig.Derivatives and Integrals of Inverse Trig Functions.Exponential and Logarithmic Differentiation.Differentials, Linear Approximation, Error Propagation.Curve Sketching, Rolle’s Theorem, Mean Value Theorem.Implicit Differentiation and Related Rates.Equation of the Tangent Line, Rates of Change.Differential Calculus Quick Study Guide.Polar Coordinates, Equations, and Graphs.Law of Sines and Cosines, and Areas of Triangles.Linear, Angular Speeds, Area of Sectors, Length of Arcs.Solution: Let a be the first term and d be the common difference of the AP. If 7 times the 7th term of an AP is equal to 11 times its 11th term, show that the 18th term of the AP is zero. Conics: Circles, Parabolas, Ellipses, Hyperbolas Here are given some questions with their solutions for practice.Graphing and Finding Roots of Polynomial Functions.Graphing Rational Functions, including Asymptotes.Rational Functions, Equations, and Inequalities.Solving Systems using Reduced Row Echelon Form.The Matrix and Solving Systems with Matrices.Advanced Functions: Compositions, Even/Odd, Extrema.Solving Radical Equations and Inequalities.A sequence is an ordered list of items in mathematics. Solving Absolute Value Equations and Inequalities Important Questions for Class 11 Maths Chapter 9: Sequences and Series are provided in the article.Imaginary (Non-Real) and Complex Numbers.Solving Quadratics, Factoring, Completing Square.Introduction to Multiplying Polynomials.Scatter Plots, Correlation, and Regression.Algebraic Functions, including Domain and Range. ![]() Systems of Linear Equations and Word Problems.Introduction to the Graphing Display Calculator (GDC).Direct, Inverse, Joint and Combined Variation.Coordinate System, Graphing Lines, Inequalities. ![]()
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |