In the following series only one number is wrong. Find out the wrong number.
`"7 , 12 ,40, 222 , 1742 , 17390 , 208608"`

Options

A. 7
B. 12
C. 40
D. 1742

Answer

To find the wrong number in the series: `7, 12, 40, 222, 1742, 17390, 208608`, we will analyze the pattern step by step.

### Step 1: Identify the pattern
We start with the first number, 7.

### Step 2: Calculate the next number
To get from 7 to 12:
- We can use the formula: \( 7 \times 2 - 2 = 12 \)

### Step 3: Calculate the next number
Next, to get from 12 to 40:
- We can use the formula: \( 12 \times 4 - 8 = 40 \)

### Step 4: Calculate the next number
Now, to get from 40 to 222:
- We can use the formula: \( 40 \times 6 - 18 = 222 \)

### Step 5: Calculate the next number
Next, to get from 222 to the next number:
- We should calculate \( 222 \times 8 - 32 \)
- \( 222 \times 8 = 1776 \)
- \( 1776 - 32 = 1744 \)

### Step 6: Identify the discrepancy
Now we compare this with the given number in the series, which is 1742.
- Since 1742 is not equal to 1744, we identify that 1742 is the wrong number in the series.

### Step 7: Verify the next number
To ensure the series continues correctly:
- The next number after 1744 should be calculated as \( 1744 \times 10 - 64 \)
- \( 1744 \times 10 = 17440 \)
- \( 17440 - 64 = 17376 \)

### Conclusion
Thus, the wrong number in the series is **1742**.