The first three terms of a proportion are 12. 21 and 8 respectively. The 4th term is

Options

A. 18
B. 16
C. 14
D. 20

Answer

To find the fourth term of the proportion given the first three terms (12, 21, and 8), we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Proportions**:
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 as:
\[ \frac{a}{b} = \frac{c}{d} \]
where \( a = 12 \), \( b = 21 \), \( c = 8 \), and \( d \) is the term we need to find.

2. **Setting Up the Equation**:
Based on the above understanding, we can set up the equation:
\[ \frac{12}{21} = \frac{8}{d} \]

3. **Cross Multiplying**:
To solve for \( d \), we will cross multiply:
\[ 12 \times d = 21 \times 8 \]

4. **Calculating the Right Side**:
Now, calculate \( 21 \times 8 \):
\[ 21 \times 8 = 168 \]
So, we have:
\[ 12d = 168 \]

5. **Isolating \( d \)**:
To find \( d \), divide both sides of the equation by 12:
\[ d = \frac{168}{12} \]

6. **Performing the Division**:
Now, calculate \( \frac{168}{12} \):
\[ d = 14 \]

### Final Answer:
The fourth term is \( 14 \).