In math, we can play around with sequences in different ways. Here are some key ideas:

1. Adding Sequences: When you take two sequences, let’s call them $a_n$ and $b_n$, you can add them together. This gives you a new sequence, $c_n = a_n + b_n$.

2. Multiplying by a Number: You can also multiply a sequence by a number, which we’ll call $k$. So, if you have a sequence $a_n$, the new sequence will be $c_n = k \cdot a_n$.

3. Joining Sequences: This is where you take two sequences and stick them together to make a longer one. For example, if you have sequence $A = \{a_1, a_2\}$ and sequence $B = \{b_1, b_2\}$, you can create sequence $C = \{a_1, a_2, b_1, b_2\}$.

4. Special Patterns, or Recurrence Relations: Some sequences follow special rules. Take the Fibonacci sequence as an example. Each number is found using the two numbers before it: $F_n = F_{n-1} + F_{n-2}$. It starts with $F_0 = 0$ and $F_1 = 1$.

5. Changing Sequences: You can change sequences in different ways, like flipping them around or moving the numbers to different spots.

These ideas help us understand how sequences work in math!