![]() I would explain to the students that now that we have the formula we can easily find the nth term that contains our sum, and this parallels the same process as having an x value and finding a corresponding y value and by using this process I can assure the students that the methods they learned in algebra are still important in pre-calculus. Then just like the students did in algebra one, they can use the point slope formula to come up with an equation for the sequence. After writing out a few terms, I would expect the students to find the common difference between the terms and then compute the slope of the terms (I say slope because I hope they can see that this pattern is linear and therefore we can model the data using a linear equation and not just use the formula for arithmetic sequence but rather derive one ourselves). Q’s first bill happens to be $65, his total after the second bill is $130, after the third bill the running sum is $195, if this pattern continues, how many months will it take for the total to reach $780? To solve this problem we would write the terms in a sequence starting with the first term being $65 and up to three more terms. ![]() For this example, lets suppose that John Q, a pre-calculus student, has just bought a new phone from apple, but because of this new upgrade, Q’s parents are concern with the sum of money they will be paying for his monthly bill. There are many word problems we can do with arithmetic sequences but I am going to give one example that I believe students will understand. ![]() “What interesting word problems using this topic can your students do now?” His topic, from Precalculus: arithmetic sequences. This student submission comes from my former student Erick Cordero. I plan to share some of the best of these ideas on this blog (after asking my students’ permission, of course). Instead, I asked my students to think about three different ways of getting their students interested in the topic in the first place. In other words, the point of the assignment was not to devise a full-blown lesson plan on this topic. Notation will include Σ and a n.In my capstone class for future secondary math teachers, I ask my students to come up with ideas for engaging their students with different topics in the secondary mathematics curriculum. AII.16 The student will investigate and apply the properties of arithmetic and geometric sequences and series to solve practical problems, including writing the first n terms, finding the nth term, and evaluating summation formulas.AII.03b The student will write radical expressions as expressions containing rational exponents and vice versa.AII.03a The student will add, subtract, multiply, divide, and simplify radical expressions containing positive rational numbers and variables and expressions containing rational exponents.AII.02 The student will add, subtract, multiply, divide, and simplify rational expressions, including complex fractions. ![]() AII.01 The student will identify field properties, axioms of equality and inequality, and properties of order that are valid for the set of real numbers and its subsets, complex numbers, and matrices.7.20 The student will write verbal expressions as algebraic expressions and sentences as equations.7.19 The student will represent, analyze, and generalize a variety of patterns, including arithmetic sequences and geometric sequences, with tables, graphs, rules, and words in order to investigate and describe functional relationships.
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