In each of the following number series , a wrong number is given ,find out the wrong number -----
1 3 6 11 20 39 70

Options

A. 3
B. 39
C. 11
D. 20

Answer

To find the wrong number in the series: 1, 3, 6, 11, 20, 39, 70, we will analyze the pattern of the series step by step.

### Step 1: Identify the pattern
Let's look at the differences between consecutive numbers in the series:
- 3 - 1 = 2
- 6 - 3 = 3
- 11 - 6 = 5
- 20 - 11 = 9
- 39 - 20 = 19
- 70 - 39 = 31

So, the differences are: 2, 3, 5, 9, 19, 31.

### Step 2: Analyze the differences
Now, let's look at the differences between these differences:
- 3 - 2 = 1
- 5 - 3 = 2
- 9 - 5 = 4
- 19 - 9 = 10
- 31 - 19 = 12

So, the second differences are: 1, 2, 4, 10, 12.

### Step 3: Identify a pattern in the second differences
The second differences do not seem to follow a clear pattern. Let's look at the original differences again:
- The differences between the numbers seem to be increasing, but not in a consistent manner.

### Step 4: Check for a consistent multiplication and addition pattern
From the original series, we can try to establish a multiplication and addition pattern:
1. Start with 1:
- 1 * 2 + 1 = 3
2. Next, take 3:
- 3 * 2 = 6
3. Next, take 6:
- 6 * 2 - 1 = 11
4. Next, take 11:
- 11 * 2 - 2 = 20
5. Next, take 20:
- 20 * 2 - 3 = 37 (This is where we find a discrepancy)

### Step 5: Identify the wrong number
Following the established pattern:
- The next number after 20 should be 37 (not 39).
- Therefore, the wrong number in the series is **39**.

### Conclusion
Thus, the wrong number in the series 1, 3, 6, 11, 20, 39, 70 is **39**.

---