The first, second and fourth terms of a propation are 5,15 and 90 respectively. Find the third term.

Answer

To solve the problem, we need to find the third term of a proportion where the first term is 5, the second term is 15, and the fourth term is 90. We will denote the third term as \( x \).

### Step-by-Step Solution:

1. **Identify the Terms**:
- First term (a) = 5
- Second term (b) = 15
- Third term (c) = \( x \) (unknown)
- Fourth term (d) = 90

2. **Set Up the Proportion**:
In a proportion, the product of the extremes is equal to the product of the means. This can be expressed as:
\[ a \cdot d = b \cdot c \]
Substituting the known values:
\[ 5 \cdot 90 = 15 \cdot x \]

3. **Calculate the Product of the Extremes**:
\[ 5 \cdot 90 = 450 \]
So, we have:
\[ 450 = 15 \cdot x \]

4. **Solve for \( x \)**:
To find \( x \), divide both sides of the equation by 15:
\[ x = \frac{450}{15} \]

5. **Perform the Division**:
\[ x = 30 \]

6. **Conclusion**:
The third term of the proportion is \( x = 30 \).

### Final Answer:
The third term is **30**.

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