Find the wrong term
9, 15, 27, 51, 101, 195

Options

A. 9
B. 15
C. 27
D. 101

Explanation

To find the wrong term in the series 9, 15, 27, 51, 101, 195, we will analyze the differences between the consecutive terms step by step.

### Step 1: Identify the series
The given series is:
\[ 9, 15, 27, 51, 101, 195 \]

### Step 2: Calculate the differences between consecutive terms
Let's calculate the differences:
- Difference between 15 and 9:
\[ 15 - 9 = 6 \]
- Difference between 27 and 15:
\[ 27 - 15 = 12 \]
- Difference between 51 and 27:
\[ 51 - 27 = 24 \]
- Difference between 101 and 51:
\[ 101 - 51 = 50 \]
- Difference between 195 and 101:
\[ 195 - 101 = 94 \]

So, the differences are:
\[ 6, 12, 24, 50, 94 \]

### Step 3: Analyze the pattern of differences
Now, let's look at the differences:
- The first difference is 6.
- The second difference is 12 (which is \(6 \times 2\)).
- The third difference is 24 (which is \(12 \times 2\)).
- The fourth difference is 50, which does not follow the pattern of doubling.

### Step 4: Identify the expected difference
If we follow the pattern of doubling:
- The difference after 24 should be:
\[ 24 \times 2 = 48 \]
- The next term after 51 should be:
\[ 51 + 48 = 99 \]

### Step 5: Check the next term
Continuing the pattern:
- The next difference after 48 should be:
\[ 48 \times 2 = 96 \]
- Adding this to our expected term:
\[ 99 + 96 = 195 \]

### Step 6: Identify the wrong term
From our analysis:
- The term 101 should actually be 99.
- Therefore, the wrong term in the series is:
\[ \text{Wrong term} = 101 \]

### Conclusion
The wrong term in the series is **101**, which should be replaced by **99**.

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