The resource at the bottom is a formula chart for geometric and arithmetic sequences and series. The third resource is an arithmetic and geometric sequence and series game. The second resource would be a great follow up after teaching arithmetic sequences. I’m working on the geometric sequence activity now and hope to finish in a week or so. I’ve attached a couple more of my resources. I wanted to create something that students could learn from and see how these patterns are involved in real-life situations. When I was creating this resource, it really stretched my thinking. The the number of terms is a sequence is found. Some of the examples I used above are in my Arithmetic Sequence Activity seen below. This video explains how to determine a recursive definition and a closed formula for an arithmetic sequence. Students need to know that their math is real and useful! I hope this encourages you to use some of these examples or make up some of your own. It’s really fun to create these problems. I hope I’ve given you plenty to think about. To do this, its easiest to plug our recursive formula into a. We often want to find an explicit formula for bn, which is a formula for which bn1,bn2,b1,b0 dont appear. because bn is written in terms of an earlier element in the sequence, in this case bn1. When you are finished reading this post, please consider filling out this feedback form called: Understanding Our Visitors. An example of a recursive formula for a geometric sequence is. I’m happy for you to use these situations with your classes. Yes, but I want visuals! I also did not want the situation to be a direct variation or always positive numbers and always increasing or positive slopes.īelow are some of the situations I’ve come up with along with a picture. My recent thoughts have been about arithmetic sequences. recursive definition for a sequence is a definition that includes the value of one or more initial terms of the sequence and a formula. I’ve also tried to catch the situation in action, but it’s not always possible especially since sometimes I think of an idea while driving or when I’m falling asleep at night. I’ve made it a goal of mine to find real-life situations. When I was in college and the earlier part of my teaching career, I was all about the math… not how I might could use it in real life. The recursive formula for a sequence allows you to find the value of the n th term in the sequence if you know the value of the (n-1) th term in the sequence.Ī sequence is an ordered list of numbers or objects.One of my goals as a math teacher is to present real-life math every chance I get. and are often referred to as positive integers. The natural numbers are the numbers in the list 1, 2, 3. The sum of an arithmetic progression from a given starting. The natural numbers are the counting numbers and consist of all positive, whole numbers. Our printable recursive sequence worksheets provide ample practice for high school students on various topics like writing arithmetic sequence, geometric sequence and general sequence using the recursive formula, determining the recursive formula for the given sequences, finding the specific term and more. Sal finds an explicit formula of a geometric sequence given the first few terms of the sequences. The index of a term in a sequence is the term’s “place” in the sequence. Geometric sequences are also known as geometric progressions. For example in the sequence 2, 6, 18, 54., the common ratio is 3.Įxplicit formulas define each term in a sequence directly, allowing one to calculate any term in the sequence without knowing the value of the previous terms.Ī geometric sequence is a sequence with a constant ratio between successive terms. For example: In the sequence 5, 8, 11, 14., the common difference is "3".Įvery geometric sequence has a common ratio, or a constant ratio between consecutive terms. Arithmetic sequences are also known are arithmetic progressions.Įvery arithmetic sequence has a common or constant difference between consecutive terms. \)Īn arithmetic sequence has a common difference between each two consecutive terms.
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