![]() The Golden Ratio is a proportion that is considered to be the most pleasing ratio to the human eye! You may also know the Golden Ratio as the golden mean, the divine proportion, phi, or the Greek letter ϕ. Now that we know the secret pattern behind this sequence, let’s look at why the Fibonacci sequence is so special! The Fibonacci sequence’s main claim to fame is that it is found throughout art, architecture and even in nature via the golden ratio. Take a look at how this sequence works below: Why is the Fibonacci Sequence Famous? The next term of the Fibonacci sequence is 21! The pattern of this famous sequence is all about adding the two previous terms together. Basically, we know that the geometric series gives us the following terms: If the idea of converging or diverging to infinity, doesn’t make sense yet, that’s ok, keep reading and we’ll go over everything! Infinite Geometric Series:Īn infinite geometric series happens when we take the terms of a geometric sequence, and we sum them together, all of them together, starting with the first term, going all the way to infinity. On the other hand, an infinite sequence that is also a geometric sequence, can either diverge to infinity, or converge to a number. When it comes to adding an infinite arithmetic sequence together, the arithmetic sequence always diverges to infinity. But now, we want to ask ourselves, what would happen if we were to add an entire infinite sequence, by adding together each term within the sequence? We have already seen examples of this earlier in this post when looking at an arithmetic sequence or geometric sequence. If we were to find the next term in the example of the sequence below, the next term of the sequence would be 12 (10+2=12).Īn infinite sequence is one in which the sequence just keeps going and going infinitely with no end. The number we add to each term in this sequence (in this case 2), is called the common difference. ![]() Notice we are adding 2 to each term in the sequence 4, 6, 8, 10, … below. Take a look at the example of the of the arithmetic sequence below. Infinite Geometric Series Special Sequencesįibonacci Sequence Summing Every number from 1 to 100 Arithmetic Sequence:Īrithmetic sequences are a sequence of numbers that form a pattern when the same number is either added or subtracted to each successive term. A sequence can be based on addition, subtraction, multiplication, division, or even based on the value of the previous term! Let’s take a look at each type of sequence one step at a time with an example for each: Types of SequencesĪrithmetic Sequence Geometric Sequence Recursive Sequence Finite Sequencesįinite Arithmetic Series Finite Geometric Series Infinite Sequences ![]() There are so many different types of sequences! Sequences can take so many different forms, they can be infinite sequence where they can go on forever, or they can be finite sequence where they have an end. After reading this post, see if you can come up with your own sequence to add to their encyclopedia! Types of Sequences: The above examples of sequences are just a snippet of what a sequence can look like, but there are so many sequences that exist! There is even a website that compiles every sequence in the world possible, called The On-Line Encyclopedia of Integer Sequences (OEIS), it’s like a kind of dictionary but for sequences! They also accept new sequences to their website.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |