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The problem in the image is about an arithmetic series and is stated as follows:

**Problem:**
The sum of the third, fourth, and fifth terms of an arithmetic series is 99. If the first term is 3, find the value of the fifth term.

### Step-by-Step Solution:

1. **General form of an arithmetic sequence:**
   The \(n\)-th term of an arithmetic sequence is given by:
   \[
   a_n = a_1 + (n-1) \cdot d
   \]
   where:
   - \(a_1\) is the first term,
   - \(d\) is the common difference,
   - \(n\) is the position of the term in the sequence.

2. **Define the terms:**
   Given that the first term \(a_1 = 3\):
   - The third term: \(a_3 = a_1 + 2d = 3 + 2d\),
   - The fourth term: \(a_4 = a_1 + 3d = 3 + 3d\),
   - The fifth term: \(a_5 = a_1 + 4d = 3 + 4d\).

3. **Sum of the third, fourth, and fifth terms:**
   According to the problem, the sum of the third, fourth, and fifth terms is 99:
   \[
   a_3 + a_4 + a_5 = 99
   \]
   Substituting the values of \(a_3\), \(a_4\), and \(a_5\):
   \[
   (3 + 2d) + (3 + 3d) + (3 + 4d) = 99
   \]
   Simplify:
   \[
   9 + 9d = 99
   \]
   Solve for \(d\):
   \[
   9d = 99 - 9
   \]
   \[
   9d = 90
   \]
   \[
   d = 10
   \]

4. **Find the fifth term:**
   Now that we have the common difference \(d = 10\), we can find the fifth term:
   \[
   a_5 = 3 + 4 \cdot 10 = 3 + 40 = 43
   \]

### Final Answer:
The value of the fifth term is **43**.

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Would you like more details or have any questions?  
Here are 5 related questions you might want to explore:
1. How do you derive the formula for the \(n\)-th term of an arithmetic sequence?
2. What happens if the common difference \(d\) is negative?
3. How do you find the sum of the first \(n\) terms of an arithmetic sequence?
4. What are some real-life applications of arithmetic sequences?
5. How does this method change if we are working with a geometric sequence instead?

**Tip:** Always double-check the arithmetic calculations while solving equations involving series to avoid small errors.

The sum of the third, fourth, and fifth terms of an arithmetic series is 99. If the first term is 3, then find the value of the fifth term.

Learn how to find the fifth term of an arithmetic series where the sum of the third, fourth, and fifth terms is 99, and the first term is given as 3. This problem involves algebraic techniques and arithmetic sequence formulas, suitable for students in Grades 7-9.

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