If x, 18, 108 are in the continued Proportion, find the value of x.

Answer

To solve the problem where \( x, 18, 108 \) are in continued proportion, we can follow these steps:

### Step 1: Understand the concept of continued proportion
In continued proportion, if \( a, b, c \) are in continued proportion, then the ratio \( \frac{a}{b} = \frac{b}{c} \).

### Step 2: Set up the equation
For the numbers \( x, 18, 108 \), we can set up the equation as follows:
\[ \frac{x}{18} = \frac{18}{108} \]

### Step 3: Simplify the right side of the equation
Now, simplify the right side:
\[ \frac{18}{108} = \frac{1}{6} \]
So, the equation now looks like:
\[ \frac{x}{18} = \frac{1}{6} \]

### Step 4: Cross-multiply
Now, we will cross-multiply to solve for \( x \):
\[ x \cdot 6 = 18 \cdot 1 \]
This simplifies to:
\[ 6x = 18 \]

### Step 5: Solve for \( x \)
Now, divide both sides by 6 to find \( x \):
\[ x = \frac{18}{6} = 3 \]

### Final Answer
Thus, the value of \( x \) is \( 3 \).

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