To find the wrong number in the series: 9, 19, 37, 75, 149, 297, we will analyze the pattern in the series step by step.
### Step 1: Identify the pattern
Let's look at the differences between consecutive terms in the series.
- The first term is 9.
- The second term is 19.
- The third term is 37.
- The fourth term is 75.
- The fifth term is 149.
- The sixth term is 297.
### Step 2: Calculate the differences
Now, let's calculate the differences between each pair of consecutive terms:
1. \( 19 - 9 = 10 \)
2. \( 37 - 19 = 18 \)
3. \( 75 - 37 = 38 \)
4. \( 149 - 75 = 74 \)
5. \( 297 - 149 = 148 \)
So, the differences are: 10, 18, 38, 74, 148.
### Step 3: Analyze the differences
Now, let's look at the pattern in the differences:
- The first difference is 10.
- The second difference is 18.
- The third difference is 38.
- The fourth difference is 74.
- The fifth difference is 148.
### Step 4: Check for a consistent pattern
We can see that the differences are not consistent. Let's see if there's a pattern in the differences of the differences:
1. \( 18 - 10 = 8 \)
2. \( 38 - 18 = 20 \)
3. \( 74 - 38 = 36 \)
4. \( 148 - 74 = 74 \)
The second differences are: 8, 20, 36, 74.
### Step 5: Identify the wrong number
Now let's analyze the second differences:
1. The difference between 8 and 20 is 12.
2. The difference between 20 and 36 is 16.
3. The difference between 36 and 74 is 38.
The second differences are not following a clear pattern either. However, if we look closely at the terms, we can see that if we take the term before 297, which is 149, and double it, we get 298.
Thus, the last term in the series should be 298 instead of 297.
### Conclusion
The wrong number in the series is **297**.
