Arithmetic and Geometric Sequences and Series; （算术和几何序列和系列;）.pdfVIP

Mathematics Enhanced Scope and Sequence –Algebra II Arithmetic and Geometric Sequences and Series Reporting Category Expressions and Operations Topic Exploring sequences and series Primary SOL AII.2 The student will investigate and apply the properties of arithmetic and geometric sequences and series to solve real-world problems, including writing the first n terms, finding the nth term, and evaluating summation formulas. Notation will include ∑ and a . n Materials Graphing calculators Four attached handouts Vocabulary recursive formula, explicit formula, sequence, series, arithmetic sequence, arithmetic series, infinite series, geometric sequence, geometric series (AII.2) Student/Teacher Actions (what students and teachers should be doing to facilitate learning) DAYS 1AND 2 1. Teach the basics of arithmetic and geometric sequences and series, making sure students fully understand the formulas and sigma notation. DAY 3 1. Distribute copies of the attached Tic-Tac-Toe handout, and tell students they will be playing the game after completing the handout. While students are working, write the following 63 8 3 425 numbers on the board in a 4 x 3 array: , 3, , 2, , 5, 7, 16, 18, 49, , 360 16 3 5 16 2. When students have completed the handout, direct them to check to see that they have the 12 numbers written on the board as their answers . If any of their answers are different, have them check their work and/or a