Sequences algebra1/14/2024 ![]() ![]() Sequence, I could define it as a sub k from k equals 1 toĤ, with- instead of explicitly writing the numbers It defining our sequence as explicitly using kind of aįunction notation or something close to function notation. ![]() Now, I could also define itīy not explicitly writing the sequence like this. So this just says, all of theĪ sub k's from k equals 1, from our first term, all This right over here is the sequence a sub kįor k is going from 1 to 4, is equal to thisĪt it this way, we can look at each of these as But I want to make usĬomfortable with how we can denote sequences andĪlso how we can define them. Of different notations that seem fancy forĭenoting sequences. So we could call thisĪn infinite sequence. Pattern going on and on and on, I'll put three dots. This is infinite, to show that we keep this Keep adding the same amount, we call these Infinite sequence- let's say we start atģ, and we keep adding 4. So this one we wouldĬall a finite sequence. And let's say I only have theseįour terms right over here. Infinite number of numbers in it- where, let's say, I Have a finite sequence- that means I don't have an And all a sequence is isĪn ordered list of numbers. Video is familiarize ourselves with the notion of a sequence. I assume for quizzes however that they will continue to specify the start 1, so just work around it. You can easily avoid this problem in your own work by explicitly starting your K to start at 0. In modern Computer Science(Programming), we don't work with Indexes like this any longer, and starting an Index at 1 is generally fallen out of fashion largely in part of this constant need to work around the problem. We need to subtract 1 to bring back that balance. The current Index can be seen as offset by 1 due to starting at 1. If We look at K=1 and did not subtract 1 from the current index we would actually get 1+3(1) = 4 or 1+3(2)=7. This number increments each time across the "loop" and can be seen as similar to the Sigma∑ notation's looping functionality in that respect.) PreNote: ( k=1 is an index location, like finding a book in a library. This is essentially a "hack" to avoid counting your current "index" location against the math. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution License. Use the information below to generate a citation. ![]() ![]() Then you must include on every digital page view the following attribution: If you are redistributing all or part of this book in a digital format, Then you must include on every physical page the following attribution: If you are redistributing all or part of this book in a print format, Want to cite, share, or modify this book? This book uses the You can choose any term of the sequence, and add 3 to find the subsequent term. In this case, the constant difference is 3. The sequence below is another example of an arithmetic sequence. For this sequence, the common difference is –3,400. Each term increases or decreases by the same constant value called the common difference of the sequence. The values of the truck in the example are said to form an arithmetic sequence because they change by a constant amount each year. In this section, we will consider specific kinds of sequences that will allow us to calculate depreciation, such as the truck’s value. The truck will be worth $21,600 after the first year $18,200 after two years $14,800 after three years $11,400 after four years and $8,000 at the end of five years. The loss in value of the truck will therefore be $17,000, which is $3,400 per year for five years. After five years, she estimates that she will be able to sell the truck for $8,000. One method of calculating depreciation is straight-line depreciation, in which the value of the asset decreases by the same amount each year.Īs an example, consider a woman who starts a small contracting business. This decrease in value is called depreciation. The book-value of these supplies decreases each year for tax purposes. Use an explicit formula for an arithmetic sequence.Ĭompanies often make large purchases, such as computers and vehicles, for business use.Use a recursive formula for an arithmetic sequence.Find the common difference for an arithmetic sequence. ![]()
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