Find the missing term in the following numbers series:
18,?,9,18,72,576

Options

A. A)12
B. B)9
C. C)18
D. D)10

Answer

To find the missing term in the series: 18, ?, 9, 18, 72, 576, we can follow these steps:

### Step 1: Identify the known terms
The series we have is:
- 1st term: 18
- 2nd term: ?
- 3rd term: 9
- 4th term: 18
- 5th term: 72
- 6th term: 576

### Step 2: Look for a pattern
We need to find a relationship between the terms. Let's analyze the sequence:
- From 18 (1st term) to 9 (3rd term), we can see that 9 is half of 18.
- From 9 (3rd term) to 18 (4th term), we can see that 18 is double 9.
- From 18 (4th term) to 72 (5th term), we can see that 72 is four times 18.
- From 72 (5th term) to 576 (6th term), we can see that 576 is eight times 72.

### Step 3: Establish the multiplication pattern
The pattern we observe is:
- 18 to 9: divided by 2 (or multiplied by 1/2)
- 9 to 18: multiplied by 2
- 18 to 72: multiplied by 4
- 72 to 576: multiplied by 8

The multipliers are 1/2, 2, 4, and 8, which are powers of 2 (specifically, 2^(-1), 2^1, 2^2, and 2^3).

### Step 4: Determine the missing term
To find the missing term (let's call it K), we can use the established pattern:
- The term before 9 (which is K) should be multiplied by 2 to get 9.

Thus, we can set up the equation:
\[ K \times 2 = 9 \]
\[ K = \frac{9}{2} = 4.5 \]

### Step 5: Verify the pattern
Now, let's check if this fits into the sequence:
- Starting with 18, if we multiply by 1/2 (which gives us K = 4.5), we get:
- 18 * (1/2) = 9 (which is the 3rd term)
- Then, if we multiply 9 by 2, we get:
- 9 * 2 = 18 (which is the 4th term)
- Continuing, if we multiply 18 by 4, we get:
- 18 * 4 = 72 (which is the 5th term)
- Finally, if we multiply 72 by 8, we get:
- 72 * 8 = 576 (which is the 6th term)

The pattern holds true.

### Conclusion
The missing term in the series is **4.5**.

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