Find the value of a given that 3, a, 5, 20 are in proportion.

Answer

To find the value of \( a \) given that \( 3, a, 5, 20 \) are in proportion, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Proportion**: When four numbers \( a, b, c, d \) are in proportion, it means that the ratio of the first two numbers is equal to the ratio of the last two numbers. Mathematically, this can be expressed as:
\[ \frac{a}{b} = \frac{c}{d} \]
In our case, we have \( 3, a, 5, 20 \). So we can write:
\[ \frac{3}{a} = \frac{5}{20} \]

2. **Cross-Multiplying**: To eliminate the fractions, we can cross-multiply:
\[ 3 \times 20 = a \times 5 \]
This simplifies to:
\[ 60 = 5a \]

3. **Solving for \( a \)**: Now, we need to isolate \( a \). We do this by dividing both sides of the equation by 5:
\[ a = \frac{60}{5} \]
Simplifying this gives:
\[ a = 12 \]

4. **Conclusion**: Therefore, the value of \( a \) is \( 12 \).

### Final Answer:
\[ a = 12 \]