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!