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The image asks to write the arithmetic series \(6 + 12 + 18 + 24 + 30 + 36 + 42\) in summation notation.

This is an arithmetic sequence where:
- The first term \(a = 6\)
- The common difference \(d = 6\)

The general formula for the \(n\)-th term of an arithmetic sequence is:
\[
a_n = a + (n - 1) d
\]
Substituting \(a = 6\) and \(d = 6\), the formula becomes:
\[
a_n = 6 + (n - 1) \cdot 6 = 6n
\]
The given sequence has 7 terms (from \(n = 1\) to \(n = 7\)).

Thus, the summation notation for this series is:
\[
\sum_{n=1}^{7} 6n
\]

Would you like further details or have any questions?

Here are 5 related questions for further practice:
1. What is the sum of this arithmetic series?
2. How do you find the sum of any arithmetic series?
3. Can you express the series \(4 + 8 + 12 + 16 + 20\) in summation notation?
4. What is the 10th term of the arithmetic sequence with first term 6 and common difference 6?
5. What is the general form of an arithmetic series?

**Tip**: To find the sum of an arithmetic series, you can use the formula \(S_n = \frac{n}{2} (a + l)\), where \(l\) is the last term.

Write the arithmetic series 6 + 12 + 18 + 24 + 30 + 36 + 42 in summation notation.

Learn how to express the arithmetic series 6 + 12 + 18 + 24 + 30 + 36 + 42 in summation notation. This problem explores the basic concepts of arithmetic sequences and their summation, making it perfect for students in Grades 6-8.

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