Write the following series in sigma notation.
8, plus, 15, plus, 22, plus, 29, plus, 36
8+15+22+29+36

The given series is:

\[ 8 + 15 + 22 + 29 + 36 \]

This series is an **arithmetic sequence** with the first term \( a = 8 \) and a common difference \( d = 7 \).

We can express this series in **sigma notation** as:

\[
\sum_{n=1}^{5} \left( 7n + 1 \right)
\]

### Explanation:
- The formula for the \(n\)-th term of an arithmetic sequence is given by:
  \[ a_n = a + (n-1) \cdot d \]
  Substituting \( a = 8 \) and \( d = 7 \), we get:
  \[ a_n = 8 + (n-1) \cdot 7 = 7n + 1 \]

Thus, the series can be written as:

\[
\sum_{n=1}^{5} (7n + 1)
\]

Would you like further details or have any questions?

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Here are 5 related questions for you to explore:
1. How do you find the sum of an arithmetic series using the formula?
2. What is the general form for writing a geometric series in sigma notation?
3. How do you identify if a series is arithmetic or geometric?
4. What is the difference between sigma notation and product notation?
5. How would you express a series with a quadratic pattern in sigma notation?

**Tip**: When working with arithmetic sequences, remember that the common difference \(d\) plays a crucial role in defining the pattern!

Write the following series in sigma notation. 8, plus, 15, plus, 22, plus, 29, plus, 36

Learn how to write the arithmetic series 8, 15, 22, 29, 36 in sigma notation. This step-by-step guide covers essential concepts, including identifying the first term, calculating the common difference, and expressing the series using sigma notation. Suitable for students in Grades 8-10.

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