The series $8 + 12 + 16 + 20$ can be expressed in sigma notation as follows:

$\sum_{n=1}^{4} (4n + 4)$

Explanation:

• This is an arithmetic series with a common difference of 4.
• The general term of this sequence can be written as $4n + 4$, where $n$ starts from 1 and goes to 4.

Would you like further details or have any questions?

Here are 5 questions to expand on this concept:

1. How would you express a longer arithmetic series using sigma notation?
2. Can you explain how to find the sum of an arithmetic series?
3. What is the general form for the $n$-th term of an arithmetic sequence?
4. How do you derive the formula for the sum of an arithmetic sequence?
5. How does changing the common difference affect the series?

Tip: When working with arithmetic sequences, identifying the common difference helps you quickly form the general term for sigma notation.