Write the following series in sigma notation.
3, plus, 12, plus, 21, plus, 30, plus, 39, plus, 48
3+12+21+30+39+48

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!

Write the following series in sigma notation. 3 + 12 + 21 + 30 + 39 + 48

Learn how to express the arithmetic series 3 + 12 + 21 + 30 + 39 + 48 in sigma notation. This problem covers arithmetic sequences, including how to find the general term and sum in sigma form. Suitable for Grades 9-12.

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