find the sum of an arithmetic series with the given number of terms, a1 and an. 9 terms; 2,5,8,11

To find the sum of an arithmetic series, we use the formula:

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

Where:
- \(S_n\) is the sum of the arithmetic series.
- \(n\) is the number of terms.
- \(a_1\) is the first term.
- \(a_n\) is the last term.

Given:
- Number of terms, \(n = 9\)
- First term, \(a_1 = 2\)
- Last term, \(a_n = 26\)

### Steps:
1. The common difference \(d = 5 - 2 = 3\).
2. Calculate the last term \(a_n\):
   \[
   a_n = a_1 + (n-1) \cdot d = 2 + (9-1) \cdot 3 = 2 + 24 = 26
   \]
3. Now, use the sum formula:
   \[
   S_9 = \frac{9}{2} \times (2 + 26) = \frac{9}{2} \times 28 = 9 \times 14 = 126
   \]

### Answer:
The sum of the arithmetic series is \(126\).

Would you like a more detailed explanation or have further questions?

Here are some related questions:
1. How do you find the common difference in an arithmetic sequence?
2. What is the general formula to find the nth term of an arithmetic sequence?
3. How do you calculate the sum when only the first term and common difference are given?
4. What if the number of terms in the sequence is unknown? How can we find it?
5. How does the sum of an arithmetic series compare with the sum of a geometric series?

**Tip**: When calculating the sum of a series, it's important to ensure that both the first and last terms are correctly identified to avoid errors.

Find the sum of an arithmetic series with the given number of terms, a1 and an. 9 terms; 2, 5, 8, 11.

Discover how to find the sum of an arithmetic series with 9 terms, starting at 2 and increasing by a common difference of 3. Learn to apply the formula for the sum of an arithmetic series and calculate the final term using the sequence's pattern. Ideal for students in Grades 9-11.

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