To write sequences using sigma notation, also known as summation notation, you can follow these simple steps:

1. Identify the Sequence: First, clearly define the sequence you want to write down. For example, if you want the first five positive numbers, the sequence is: 1, 2, 3, 4, 5.

2. Determine the General Term: Next, find a formula that shows the $n$-th term of the sequence. In our example, the $n$-th term can be represented as $a_n = n$, which means each number is just the position in the sequence.

3. Establish the Summation Limits: Now, figure out the range of $n$ for the terms you want to add together. If you want the sum of the first five positive integers, your limits will be from $n=1$ to $n=5$.

4. Write in Sigma Notation: Put everything together into sigma notation. The sum of the first five positive integers can be written as:

   $\sum_{n=1}^{5} n$

5. Evaluate if Necessary: Sometimes, you might want to find out the total sum. For this example, the sum is $1 + 2 + 3 + 4 + 5 = 15$.

By following these steps, you can express different sequences using sigma notation. This makes it easier to understand how they work and how they relate to each other!