# Interpreting recursive equations to write a sequence that has two

The laws Complementation 1 and 2, together with the monotone laws, suffice for this purpose and can therefore be taken as one possible complete set of laws or axiomatization of Boolean algebra. Every law of Boolean algebra follows logically from these axioms. Look for and make use of structure. This is not the first time a lesson opener has been about patterns, however. They just have to fill in a few blanks in each pattern. Just as I have all year, I call these patterns on this opener. In order to get to that point, we need a reason to have such a name for something.

Students have an easy time filling in the blanks on the first two exercises, but the third one is different; I ask how so. To get from 3 to 6, we might say that we added 3 or that we multiplied by 2.

## 6 Higher-Order Functions

The next two terms depend on which of these we choose. Once we say that a sequence is arithmetic, we know more about it, and we need less information. What is an Arithmetic Sequence? Students work on the handout, collect notes and definitions, and work on problems until they have questions.

I use the Prezi to navigate the handout this is a real strength of Prezi, as opposed to traditional slides and to share key notes.

## Arithmetic Sequences

The handout is more than most students will be able to finish within a minute class period. The key is to get students asking the questions that drive the lesson.

In this narrative, I share some of my thinking about this assignment, and how I teach it, but every implementation of this lesson is different. Defining an Arithmetic Sequence When students see 2b, 2e, and 2j, they recognize patterns, and they get to put the definition of an arithmetic sequence to work.

See how this connects to the idea of a horizontal line with its slope of zero. More generally, all of these problems are great context for students to develop number sense and to feel more confident with their arithmetic skills. I note aloud that, "Everyone is comfortable with the idea of a common difference, but how do I figure out what constant term to add or subtract?

Sharing this trick serves two purposes: The last exercise is 4 is a sequence of fractions. First of all, the instruction says to "use function notation," and this trips up a few students.

Exercises 5a through 5e share a y-intercept; 5f through 5j share a common difference or slope. This is another example of how I like to expose students to an idea before naming it and explicitly teaching it. U3p2 L1 Arithmetic Sequences.Indecision and delays are the parents of failure.

The site contains concepts and procedures widely used in business time-dependent decision making such as time series analysis for forecasting and other predictive techniques.

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The Reactive Engine A. C. Kay I wish to God these calculations were executed by steam C. Babbage, The Analytical Engine. Many of the diagrams in the thesis were hand drawn. heartoftexashop.com Write a function that describes a relationship between two quantities.

(Emphasize linear, quadratic, and exponential functions). Determine an explicit expression, a recursive process, or steps for calculation from a context. In mathematics and mathematical logic, Boolean algebra is the branch of algebra in which the values of the variables are the truth values true and false, usually denoted 1 and 0 heartoftexashop.comd of elementary algebra where the values of the variables are numbers, and the prime operations are addition and multiplication, the main operations of Boolean algebra are the conjunction and denoted.

Recursive formulas for arithmetic sequences | Algebra (article) | Khan Academy