The given series is:

$3 + 12 + 21 + 30 + 39 + 48$

This can be rewritten in sigma notation by recognizing the pattern in the terms. The difference between consecutive terms is constant, meaning this is an arithmetic sequence where:

• The first term $a_1 = 3$
• The common difference $d = 9$

The general form of the $n$-th term of an arithmetic sequence is:

$a_n = a_1 + (n - 1)d$

Substituting the known values:

$a_n = 3 + (n - 1) \cdot 9 = 9n - 6$

Thus, the sum of the first 6 terms can be written in sigma notation as:

$\sum_{n=1}^{6} (9n - 6)$

Would you like more details or have any questions?

Here are some related questions:

1. How can you find the sum of an arithmetic series?
2. What is the formula for the sum of the first $n$ terms of an arithmetic sequence?
3. How do you derive the general term for an arithmetic sequence?
4. How do you recognize an arithmetic sequence from a set of numbers?
5. What is the difference between arithmetic and geometric sequences?

Tip: Always check the common difference in a series to see if it’s arithmetic!