To find the sum of the sequence $9, 13, 17, 21, 25, 29, 33$, we can use the formula for the sum of an arithmetic sequence:

$S_n = \frac{n}{2} \times (a_1 + a_n)$

where:

• $S_n$ is the sum of the sequence,
• $n$ is the number of terms,
• $a_1$ is the first term,
• $a_n$ is the last term.

Steps:

1. Identify the terms:

   • First term ($a_1$) = 9
   • Last term ($a_n$) = 33
   • Number of terms ($n$) = 7

2. Plug the values into the formula: $S_7 = \frac{7}{2} \times (9 + 33)$

3. Calculate: $S_7 = \frac{7}{2} \times 42 = \frac{7 \times 42}{2} = \frac{294}{2} = 147$

The sum of the sequence is 147.

Let me know if you want more details or have any questions. Here are some related questions:

1. How do you find the sum of an arithmetic series with more terms?
2. Can you find the sum of a geometric series?
3. What is the formula for the sum of the first $n$ terms of an arithmetic series?
4. How do you determine if a sequence is arithmetic?
5. What are the properties of an arithmetic sequence?
6. How does the formula for an arithmetic sequence change if the common difference is negative?
7. Can you sum an infinite arithmetic series?
8. How is the sum of an arithmetic series used in real-life applications?

Tip: When summing an arithmetic series, you can also add pairs from the beginning and end of the series, which will each give the same result as the sum of the first and last terms.