Write the following series in sigma notation.
7, plus, 13, plus, 19, plus, 25, plus, 31, plus, 37
7+13+19+25+31+37

The given series is:

\[ 7 + 13 + 19 + 25 + 31 + 37 \]

This is an arithmetic sequence where the first term \( a_1 = 7 \) and the common difference \( d = 6 \).

To write this in sigma notation, observe the general term of an arithmetic sequence:

\[
a_n = a_1 + (n - 1) \cdot d
\]

So for this sequence:

\[
a_n = 7 + (n - 1) \cdot 6 = 6n + 1
\]

Now, since there are 6 terms in the series, we can express the sum as:

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

This is the sigma notation for the given series.

Would you like more details or have any questions?

Here are 5 related questions:
1. How would you find the sum of an arithmetic series?
2. What is the general formula for an arithmetic sequence?
3. How do you determine the number of terms in an arithmetic series?
4. Can you express this series as a function of \( n \)?
5. What happens to the series if the common difference changes?

**Tip:** In arithmetic sequences, identifying the first term and common difference is key to writing the sequence in sigma notation!

Write the following series in sigma notation. 7 + 13 + 19 + 25 + 31 + 37

Learn how to write the series 7 + 13 + 19 + 25 + 31 + 37 in sigma notation. This problem explores arithmetic sequences, sigma notation, and the general term formula for sequences. Perfect for students in Grades 9-11.

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