Final answer:
The series 3, 6, 9, 12, 15, 18 is represented in sigma notation as Σ_{n=1}^{6} 3n, where each term can be expressed as 3 times n.
Step-by-step explanation:
To write the series 3, 6, 9, 12, 15, 18 using sigma notation, we observe the pattern that each term increases by 3. This is an arithmetic sequence with a common difference of 3. The first term, which we can denote as a1, is 3. The nth term of an arithmetic sequence is given by an = a1 + (n - 1)d, where d is the common difference. In this case, the general term can be expressed as 3n. Using sigma notation, the series is represented as Σ_{n=1}^{6} 3n where n is the index of summation indicating which term of the series is being added, and the numbers 1 and 6 are the lower and upper bounds, respectively.