In a proportion, the 1st, 2nd and 4th terms are 51, 68 and 108 respectively. Find the 3rd term.

Answer

To find the third term in the proportion where the first term is 51, the second term is 68, and the fourth term is 108, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Proportion**:
In a proportion, the relationship between the terms can be expressed as:
\[ \frac{\text{First term}}{\text{Second term}} = \frac{\text{Third term}}{\text{Fourth term}} \]
Here, we have:
- First term = 51
- Second term = 68
- Fourth term = 108
- Third term = x (unknown)

2. **Set Up the Equation**:
Using the values we have, we can set up the equation:
\[ \frac{51}{68} = \frac{x}{108} \]

3. **Cross Multiply**:
To eliminate the fractions, we can cross-multiply:
\[ 51 \times 108 = 68 \times x \]

4. **Calculate the Left Side**:
Now, calculate \(51 \times 108\):
\[ 51 \times 108 = 5508 \]

5. **Rewrite the Equation**:
Now we have:
\[ 5508 = 68 \times x \]

6. **Solve for x**:
To find x, divide both sides by 68:
\[ x = \frac{5508}{68} \]

7. **Perform the Division**:
Now, perform the division:
\[ x = 81 \]

### Final Answer:
The third term is **81**.

---