https://file.aiquickdraw.com/mathbot/file/1725655569509d6vtmlkg.jpg

From the image, the problem seems to ask you to find the value of \( a_{50} \) using the values of \( a_1 \) and \( S_{50} \).

The given information appears to be:

- \( a_1 = 6 \)
- \( S_{50} = 6650 \)
- The formula for the sum of the first \( n \) terms of an arithmetic series is \( S_n = \frac{n}{2} (a_1 + a_n) \).

Using this formula for \( S_{50} \):

\[
S_{50} = \frac{50}{2} (a_1 + a_{50})
\]

Substitute the given values \( a_1 = 6 \) and \( S_{50} = 6650 \) into the equation:

\[
6650 = \frac{50}{2} (6 + a_{50})
\]

Now, let's solve for \( a_{50} \).

\[
6650 = 25 (6 + a_{50})
\]
\[
\frac{6650}{25} = 6 + a_{50}
\]
\[
266 = 6 + a_{50}
\]
\[
a_{50} = 266 - 6
\]
\[
a_{50} = 260
\]

Thus, the value of \( a_{50} \) is 260.

Would you like a more detailed explanation of the steps or have any other questions?

Here are 5 related questions you can explore:

1. How can you find the common difference in an arithmetic series?
2. How would the formula change if this were a geometric series?
3. What is the sum of the first 100 terms in this series?
4. How can you derive the general term formula for an arithmetic sequence?
5. What happens to the sum formula if \( n \) becomes very large?

**Tip:** When solving for a term in an arithmetic series, always check whether you are working with a partial sum or individual terms to avoid confusion.

Use the values of a_1 and S_50 to find the value of a_50, given a_1 = 6 and S_50 = 6650.

Learn how to find the 50th term (a_50) of an arithmetic series using the values a_1 = 6 and S_50 = 6650. This problem involves the arithmetic series summation formula and is suitable for students in Grades 9-12.

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