Find the wrong number in the series given below:
7 8 17 45 91 172

Options

A. 45
B. 91
C. 172
D. 17

Answer

To find the wrong number in the series: 7, 8, 17, 45, 91, 172, we will analyze the pattern in the series step by step.

### Step 1: Identify the pattern
Let's look at how each number is generated from the previous number.

1. Start with the first number: **7**
2. The second number is **8**. We can see that:
\[ 7 + 1^2 = 7 + 1 = 8 \]

### Step 2: Continue the pattern
Now, let's find the next number:

3. The third number is **17**. We can see that:
\[ 8 + 3^2 = 8 + 9 = 17 \]

### Step 3: Check the next number
4. The fourth number is **45**. We will check if it follows the same pattern:
\[ 17 + 5^2 = 17 + 25 = 42 \]
Here, we see that it should be **42**, but it is **45**. This indicates that **45** is likely the wrong number.

### Step 4: Verify the subsequent numbers
5. Let's check the next number based on our found value of **42**:
\[ 42 + 7^2 = 42 + 49 = 91 \]
This matches the next number in the series.

6. Finally, check the last number:
\[ 91 + 9^2 = 91 + 81 = 172 \]
This also matches.

### Conclusion
Thus, the wrong number in the series is **45**.