Tell whether the following sequences are. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution License. Algebra 2 arithmetic and geometric sequences worksheet answers. We recommend using aĪuthors: Lynn Marecek, Andrea Honeycutt Mathis 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 In this chapter, you will review the language of algebra and take your first steps toward working with algebraic concepts. Engineers must be able to translate observations and needs in the natural world to complex mathematical commands that can provide directions to a printer.
The technology and use of 3D printers depend on the ability to understand the language of algebra. Builders have even constructed entire buildings using a 3D printer. Already, animals are benefitting from 3D-printed parts, including a tortoise shell and a dog leg. Scientists at NASA are designing ways to use 3D printers to build on the moon or Mars. This makes producing the limb less expensive and faster than conventional methods.īiomedical engineers are working to develop organs that may one day save lives. As a result, it can be printed much like you print words on a sheet of paper. This particular product is different, however, because it was developed using a 3D printer. So, that is an introduction to a geometric sequence and the general term for geometric sequence ace of n is equal to ace of 1 times r to the n minus 1.For years, doctors and engineers have worked to make artificial limbs, such as this hand for people who need them. So if we're dealing with ace of n we are just going to have r to the n minus 1. So our second term has one rate, third term has 2 rates, fourth term has 3 rates. And if you notice there's always one less rate than the term number, okay.
Eventually we're going get to our general term. Continuing down the row, a sub 4 is just going to be another rate times the previous term leaving us with a sub 1 times r cubed, so on and so forth. So what we end up with is this is equal to a sub 1 times r squared. But we know that a sub 2 is actually a sub 1 times r.
If it is, find the common ratio, the 8th term, the explicit formula, and the recursive formula. About Press Copyright Contact us Creators Advertise Developers Terms Privacy Policy & Safety How YouTube works Test new features Press Copyright Contact us Creators. So we went from 2 to 6 and then 6 to 18 we again multiplied it by that common rate 3. Algebra 2 12.2 Geometric Sequences Name ID: 1 Date Period P b2D0k1W6f GKuftDaX mScojfYtHwwanrjev LoLACo.T K QARlKlt mrpiigdhztzsJ mrBessXeNrHvnepdm. To find the third term then we take the second term and multiply it by the rate as well okay. And in order to find the second term, what we do is take that first term and multiply it by that common rate okay and then we call it r. What we're going to do now is find the general term, find the s sub n in order for a geometric sequence, okay? So we're given the first term. So I need that third term in order to figure out what exactly ki- what kind of sequence it really is, okay? I could either add 4 which would be an arithmetic sequence or multiply by 3 which tells me it's geometric. If this was just 2 terms, I wouldn't actually know what's going on because I could go from 2 to 6 one of 2 ways. 3) State the next terms in a geometric sequence. 2) State the common ratio of a geometric sequence. Okay? So that 3 is consistent so therefore I know I have a geometric sequence. Common Core State Standards: HSF-IF.A.3, HSF-BF.A.1a, HSF-BF.A.2.
12.2 GEOMETRIC SEQUENCES ALGEBRA 2 SERIES
A geometric sequence is a series of numbers where basically going from one to the next we are multiplying by a constant rate, okay? So right behind me what I have is, we're going from 2 to 6, multiplying by 3 from 6 to 18 we're multiplying by 3 as well.
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