This week in precalc 11, we reviewed for our midterm and we started our next unit. During the week, I spent a lot of time reviewing old concepts in the book and realized I forgot how to do a lot of things. The unit that I struggled reviewing the most was series and sequences.

Firstly I completely forgot the difference between a series and a sequences. The way I ended up remembering it by is that sequences are basically a list of numbers with a common difference or common ratio, and a series is a list of numbers but being added with a common difference or common ratio

Examples :

Arithmetic Sequences : $2, 4, 6, 8$

Arithmetic Series : $2 + 4 + 6 + 8$

Geometric Sequences : $3, 6, 12, 24$

Geometric Series $3 + 6 + 12 + 24$

Now I had to remember the difference between a common difference and common ratio. The common difference was for arithmetic series and sequences, it represented how much the numbers went up or down

Ex : $2, 4, 6, 8$ : the d = 2 because the numbers go up by 2

For the common ratio, it was for geometric series and sequences. It basically meant the number that was multiplied to each term.

Ex : $3, 6, 12, 24$ : the r = 2 because each number is multiplied by 2

The last thing I reviewed was converging and diverging. The most that I remembered was that one was basically getting higher or wider and the other one was getting smaller. I didn’t remember what it looked like but that’s what the reviewing was for. After looking at many examples, I made sure to know that diverging has no sum and represents either $r > 1$ or $r < -1$. For converging, I made sure to know that it does have a sum and it represents either $0 < r < 1$ or $-1 < r < 0$. For the rest, I just made sure to understand the concept of the whole unit so I can use the formulas given to figure out the answers.

There were many other things that I reviewed but these were the most important because the other units were pretty fresh in my brain. I’m glad I reviewed many days before to get used to the old concepts.