Write the following series in sigma notation.
4, plus, 13, plus, 22, plus, 31
4+13+22+31

The given series is:

\[
4 + 13 + 22 + 31
\]

This is an arithmetic sequence where the first term \(a_1 = 4\) and the common difference \(d = 9\) (since \(13 - 4 = 9\), \(22 - 13 = 9\), and so on).

We can express the general term of an arithmetic sequence as:

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

Substituting the values of \(a_1 = 4\) and \(d = 9\):

\[
a_n = 4 + (n - 1) \cdot 9 = 9n - 5
\]

Thus, the general term is \(a_n = 9n - 5\), and the sequence consists of 4 terms. Therefore, the sum can be written in sigma notation as:

\[
\sum_{n=1}^{4} (9n - 5)
\]

Would you like more details on sigma notation or how to handle other sequences?

Here are some related questions:
1. How do you find the sum of an arithmetic series?
2. What is the difference between arithmetic and geometric series?
3. Can sigma notation be used for non-arithmetic series?
4. How would the series change if the common difference were different?
5. What are the key properties of sigma notation?

**Tip**: When writing in sigma notation, always check the pattern of the sequence first—whether it's arithmetic, geometric, or something else!

Write the following series in sigma notation: 4 + 13 + 22 + 31

Learn how to write the arithmetic sequence 4 + 13 + 22 + 31 in sigma notation. This step-by-step solution covers key concepts such as arithmetic sequences, sigma notation, and the general term of a sequence. Suitable for students in Grades 9-10.

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