Arithmetic and Geometric Sequences and Series: (What I Learned)

In this unit I learned that there are easier ways to find patterns rather than manually counting them out. We instead can use formulas that use what we know to figure them out. I think that it is like a more advanced input, output table. Arithmetic Sequences are the list of the numbers in the pattern, where as the Series is the sum of the numbers. It is the same with Geometric Sequences and Series but the only difference is that Geometric is multiplying while Arithmetic is adding.

Formulas Learned:

What I need to remember most:

The main thing that I need to remember in this unit is that a Series can be convergent or divergent. When it is convergent, the common ratio will be greater than -1 but less than 1 (-1 < r < 1) and when the series is divergent, the common ratio will either be greater than 1 or less than -1 (r > 1, r < -1). With divergent series, you are only able to find the sum of the numbers/finite value; however with convergent series, not only can you find the finite value but you can also find the infinite value.