In the following number series only one number is wrong. Find out the wrong number.
`3" "35" "226" "1160" "4660" "13998`

Options

A. 13998
B. 4660
C. 226
D. 1160

Answer

To find the wrong number in the series `3, 35, 226, 1160, 4660, 13998`, we will analyze the pattern of the series step by step.

### Step 1: Identify the pattern
First, we need to observe how each number relates to the next. A common approach is to look for multiplication patterns.

### Step 2: Calculate the first multiplication
Starting with the first number:
- From 3 to 35:
- If we multiply 3 by 7, we get 21.
- Then, if we add 14 (which is 2 times 7), we get 35.

So, we can express this as:
\[ 3 \times 7 + 14 = 35 \]

### Step 3: Calculate the second multiplication
Now, let's check the next number:
- From 35 to 226:
- If we multiply 35 by 6, we get 210.
- Then, if we add 16 (which is 2 times 8), we get 226.

So, we can express this as:
\[ 35 \times 6 + 16 = 226 \]

### Step 4: Calculate the third multiplication
Next, we check:
- From 226 to 1160:
- If we multiply 226 by 5, we get 1130.
- Then, if we add 30 (which is 6 times 5), we get 1160.

So, we can express this as:
\[ 226 \times 5 + 30 = 1160 \]

### Step 5: Calculate the fourth multiplication
Now, let's check:
- From 1160 to 4660:
- If we multiply 1160 by 4, we get 4640.
- Then, if we add 20 (which is 4 times 5), we get 4660.

So, we can express this as:
\[ 1160 \times 4 + 20 = 4660 \]

### Step 6: Calculate the fifth multiplication
Finally, we check:
- From 4660 to 13998:
- If we multiply 4660 by 3, we get 13980.
- Then, if we add 18 (which is 3 times 6), we get 13998.

So, we can express this as:
\[ 4660 \times 3 + 18 = 13998 \]

### Step 7: Identify the wrong number
Now, let's summarize the calculations:
1. \( 3 \times 7 + 14 = 35 \)
2. \( 35 \times 6 + 16 = 226 \)
3. \( 226 \times 5 + 30 = 1160 \)
4. \( 1160 \times 4 + 20 = 4660 \)
5. \( 4660 \times 3 + 18 = 13998 \)

The issue arises in the second step:
- We expected \( 35 \times 6 + 16 \) to produce a number that fits the pattern. However, if we apply the consistent pattern of decreasing the multiplier by 1 each time (7, 6, 5, 4, 3), we should have had \( 35 \times 6 + 18 \) instead, which would yield 228.

Thus, the wrong number in the series is **226**; it should be **228**.

### Conclusion
The wrong number in the series is **226**.

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