In the following number series only one number is wrong. Find out the wrong number.
`4" "6" "18" "49" "201" "1011`

Options

A. 1011
B. 201
C. 18
D. 49

Answer

To find the wrong number in the series `4, 6, 18, 49, 201, 1011`, we will analyze the pattern in the series step by step.

### Step 1: Identify the pattern
Let's observe the numbers in the series:
- The first number is 4.
- The second number is 6.
- The third number is 18.
- The fourth number is 49.
- The fifth number is 201.
- The sixth number is 1011.

We need to find a consistent pattern that connects these numbers.

### Step 2: Calculate the differences
Let's look at how we can move from one number to the next:
- From 4 to 6: \(4 \times 1.5 = 6\)
- From 6 to 18: \(6 \times 3 = 18\)
- From 18 to 49: \(18 \times 2.7222 \approx 49\) (not a clear pattern)
- From 49 to 201: \(49 \times 4.0816 \approx 201\) (not a clear pattern)
- From 201 to 1011: \(201 \times 5.02985 \approx 1011\) (not a clear pattern)

### Step 3: Look for a multiplicative pattern
Instead of just differences, let's try to find a multiplicative pattern:
- From 4 to 6: \(4 \times 1.5 = 6\)
- From 6 to 18: \(6 \times 3 = 18\)
- From 18 to 49: \(18 \times 2.7222 \approx 49\) (not consistent)

This doesn't seem to yield a consistent pattern. Let's try another approach.

### Step 4: Establish a new pattern
Let's try to find a consistent way to generate the series:
1. Start with 4.
2. Multiply by 1.5 to get 6.
3. Multiply by 3 to get 18.
4. Now, let's check the next number:
- If we assume we should multiply by a consistent increment, we can try:
- \(4 \to 6\) (add 2)
- \(6 \to 18\) (add 12)
- \(18 \to 49\) (add 31)
- \(49 \to 201\) (add 152)
- \(201 \to 1011\) (add 810)

### Step 5: Identify the wrong number
Now, let's check the number that seems out of place:
- The transition from 6 to 18 seems too large compared to the others.
- If we had followed a consistent pattern, we might expect:
- From 6, if we add 9 (which is \(3^2\)), we would get 15 instead of 18.

### Conclusion
Thus, the wrong number in the series is **18**. It should have been **15**.