Find the wrong number in the following number series.
1,3,9,31,128,651,3913

Options

A. A)31
B. B)3
C. C)1
D. D)128

Answer

To find the wrong number in the series: 1, 3, 9, 31, 128, 651, 3913, we will analyze the pattern in the series step by step.

### Step 1: Identify the Pattern
We start with the first term and observe how each subsequent term is generated.

1. **First term (1)**:
- Multiply by 1 and add 2:
- \(1 \times 1 + 2 = 3\) (Second term)

2. **Second term (3)**:
- Multiply by 2 and add 3:
- \(3 \times 2 + 3 = 9\) (Third term)

3. **Third term (9)**:
- Multiply by 3 and add 4:
- \(9 \times 3 + 4 = 31\) (Fourth term)

4. **Fourth term (31)**:
- Multiply by 4 and add 5:
- \(31 \times 4 + 5 = 129\) (Expected Fifth term)

### Step 2: Check the Fifth Term
Now we check the fifth term given in the series, which is 128.

- According to the pattern, the fifth term should be 129, but the series presents it as 128.

### Step 3: Calculate the Sixth Term
To ensure consistency, we will calculate the sixth term based on our derived fifth term (129).

- **Fifth term (129)**:
- Multiply by 5 and add 6:
- \(129 \times 5 + 6 = 651\) (Sixth term, which matches the series)

### Step 4: Calculate the Seventh Term
Next, we will calculate the seventh term based on our derived fifth term (129).

- **Sixth term (651)**:
- Multiply by 6 and add 7:
- \(651 \times 6 + 7 = 3913\) (Seventh term, which matches the series)

### Conclusion
Since the pattern holds true for the sixth and seventh terms when we replace the fifth term with 129, we conclude that the wrong number in the series is:

**Wrong Number: 128**