Four terms are in proportion. The first second and fourth terms are 4, 22, and 33. Find the third term.

Options

A. 8
B. 6
C. 11
D. 3

Answer

To solve the problem where four terms are in proportion, we can follow these steps:

### Step-by-step Solution:

1. **Identify the Terms**: We have four terms in proportion. The first term (a) is 4, the second term (b) is 22, the third term (c) is unknown (let's denote it as x), and the fourth term (d) is 33. So, we can write it as:
\[ a = 4, \quad b = 22, \quad c = x, \quad d = 33 \]

2. **Set Up the Proportion**: In a proportion, the ratio of the first term to the second term is equal to the ratio of the third term to the fourth term. This can be expressed mathematically as:
\[ \frac{a}{b} = \frac{c}{d} \]
Substituting the known values, we have:
\[ \frac{4}{22} = \frac{x}{33} \]

3. **Cross-Multiply**: To solve for x, we can cross-multiply:
\[ 4 \times 33 = 22 \times x \]
This simplifies to:
\[ 132 = 22x \]

4. **Solve for x**: Now, divide both sides by 22 to isolate x:
\[ x = \frac{132}{22} \]

5. **Calculate the Value**: Performing the division:
\[ x = 6 \]

6. **Conclusion**: The third term (c) is 6.

### Final Answer:
The third term is **6**.