Pre-calc 11 Week 2

This week we learned Arithmetic sequences and series as well as Geometric sequences and series. I am going show you how to solve one of each sequence and series.

But before that, I will explain the difference between arithmetic and geometric. An Arithmetic sequence can go like so, 3,7,11,15. As you can see it goes up by 4 each time, this is called the common difference. In this sequence the first term is 3, we call this $t_1$ . An Arithmetic sequence is most commonly used for finding a term not shown in the sequence like $t_{50}$ . An Arithmetic series use the same the same rules as an Arithmetic sequence except instead of finding a term we are finding the sum of the terms between two terms like $t_1$ and $t_{50}$ . This is shown as $S_{50}$ .

Now for the Geometric sequences and series.

An example of a Geometric sequence is 3,6,12,24. Unlike an Arithmetic sequence which uses addition, Geometric uses multiplication, and instead of looking for the common difference, we are looking for the common ratio which is found by divided any two terms. For example $t_2$ / $t_1$ =3/6 which equals 2. Now a Geometric series is the sum of a Geometric Sequence.