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. For example, the sequence defined with START WITH1, INCREMENT2. When I was creating this resource, it really stretched my thinking. CREATE OR REPLACE SEQUENCE sequence-name AS INTEGER AS data-type START WITH. but there are methods that will work for certain types of sequences. Keep in mind that despite the strange notation, a sequence can be thought of as an. Some of the examples I used above are in my Arithmetic Sequence Activity seen below. If the sequence is counting something (for example, the number of polyominoes of. Sn n/2 2a1 + (n-1)d Arithmetic sequences are used in many real-world situations, such as calculating the depreciation of assets over time or the regular payment of loans. For example, the sequence 1, 1/2, 1/3, 1/4, 1/5. 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. Here, a is the first term, d is the common difference in arithmetic sequence, r is the ratio in geometric sequence and n is the number of term.I hope I’ve given you plenty to think about. We sometimes write a sequence as ( a n ), if it is finite. This means that a sequence is really a special kind of function with natural numbers as its domain. The rule should tell us how to get the thing in the n-th place, where n can be any natural number. So another way to write down a sequence is to write a rule for finding the thing in any place one wants. This does not work for an infinite sequence. If a sequence is finite, it is easy to say what it is: one can simply write down all the things in the sequence. This sequence never ends: it starts with 2, 4, 6, and so on, and one can always keep on naming even numbers. An example of a sequence that is infinite is the sequence of all even numbers, bigger than 0. ![]() The other kind is infinite sequences, which means that they keep going and never end. For example, (1, 2, 3, 4, 5) is a finite sequence. One kind is finite sequences, which have an end. Types of Sequences You need to know: Geometric Sequence is a sequence of numbers where each term after the first is found by multiplying the previous one by a number. Sequences made up of numbers are also called progressions. For example, both (Blue, Red, Yellow) and (Yellow, Blue, Red) are sequences, but they are not the same. The order that the things are in matters. The sequence (1 1 n) n 1 gets larger and larger too, but it converges. ![]() This clearly diverges by getting larger and larger. Example 4.3.1: Consider the sequence, (n) n 1. In maths, a sequence is made up of several things put together, one after the other. However there are several ways a sequence might diverge. In ordinary use, it means a series of events, one following another. An arithmetic series is one where each term is equal the one before it plus some number. It’s important to be able to identify what type of sequence is being dealt with. It is used in mathematics and other disciplines. The two main types of series/sequences are arithmetic and geometric. A sequence is a word meaning "a set of related events, movements or items that follow each other in a particular order".
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