Write the following series in sigma notation.
8, plus, 10, plus, 12, plus, 14, plus, 16, plus, 18, plus, 20
8+10+12+14+16+18+20

The series 8, 10, 12, 14, 16, 18, 20 is an arithmetic sequence where the first term \(a_1 = 8\) and the common difference \(d = 2\).

To express this series in sigma notation, we need to generalize it as a sum of terms of the form:

\[
a_n = 8 + (n-1) \cdot 2
\]

So, the general term of the sequence is:

\[
a_n = 2n + 6
\]

The sequence has 7 terms (from \(n = 1\) to \(n = 7\)).

Thus, the sigma notation for the sum is:

\[
\sum_{n=1}^{7} (2n + 6)
\]

Would you like more details or clarifications on this?

### Related questions:
1. How do you find the general term of an arithmetic sequence?
2. What is the formula for the sum of an arithmetic sequence?
3. How can you recognize arithmetic sequences from their terms?
4. How do you determine the number of terms in a series?
5. How do sigma notation and summation rules simplify the addition of sequences?

**Tip**: In an arithmetic sequence, the difference between consecutive terms remains constant.

Write the following series in sigma notation: 8 + 10 + 12 + 14 + 16 + 18 + 20

Learn how to express the arithmetic sequence 8 + 10 + 12 + 14 + 16 + 18 + 20 in sigma notation. This problem covers arithmetic sequences and sigma notation with step-by-step explanations, perfect for students in Grades 9-11.

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