Today we learned about sequences and summation notation. This is a bit of a review from Algebra 2 last year, but with a few added steps. To be able to solve a sequences and summation notation, you must start with the basics!
When given an equation, the variable n stands for the number of the term you are looking for. All you have to do is plug in the wanted term, and you are able to solve for the term needed.
Here is an example:
The next thing you are able to do with sequences, is find the nth term. Which is a term that can be found with any n given. But, sometimes you are not given an equation. When this occurs, you must first create an equation, and then plug the n in and you will get your term. In order to find the equation, you must use the terms given to you, as well as the number in the sequence they correspond to. After, you must use you brain (tough, I know) and find how the equations relate to n. Once you find your equation, you just go back to your easy ways and plug and chug and there you have your nth term!
Here is an example:
Factorials, factorials, factorials! These were not my favorite in Algebra 2, especially because they are just dumb. But, surprisingly factorials are sometimes used in sequences as well. They may be given in an equation! Just in case you forgot, a factorial (n!) means you must multiply the number given as well as the numbers preceding it. (So you might end up with a big number). But sometimes, factorials cancel out, which is great!
Here's a simple explicit formula with a factorial.
Finally, summation notation! It sounds really hard, but it is quite simple once you get it. Basically a summation notation gives you a range of numbers, which will be your n's, and an explicit formula. You must find every term needed and then add them up! And that's the answer to your summation notation! It seems a little bit confusing, but once you get it, it's a piece of cake.
Here's an example of a summation notation problem.
No comments:
Post a Comment