To find the wrong number in the series 2, 6, 10, 19, 36, 69, 134, 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 to identify a pattern.
- From 2 to 6: \(6 - 2 = 4\)
- From 6 to 10: \(10 - 6 = 4\)
- From 10 to 19: \(19 - 10 = 9\)
- From 19 to 36: \(36 - 19 = 17\)
- From 36 to 69: \(69 - 36 = 33\)
- From 69 to 134: \(134 - 69 = 65\)
### Step 2: Analyze the Differences
Now, we will analyze the differences we calculated:
- The differences are: 4, 4, 9, 17, 33, 65.
Next, let's look at the differences of these differences:
- From 4 to 4: \(4 - 4 = 0\)
- From 4 to 9: \(9 - 4 = 5\)
- From 9 to 17: \(17 - 9 = 8\)
- From 17 to 33: \(33 - 17 = 16\)
- From 33 to 65: \(65 - 33 = 32\)
### Step 3: Identify a Pattern in the Second Differences
The second differences are: 0, 5, 8, 16, 32.
Now, let's analyze the second differences:
- From 0 to 5: \(5 - 0 = 5\)
- From 5 to 8: \(8 - 5 = 3\)
- From 8 to 16: \(16 - 8 = 8\)
- From 16 to 32: \(32 - 16 = 16\)
### Step 4: Recognize the Pattern
The second differences do not show a consistent pattern. However, we notice that the first difference series seems to be increasing rapidly, suggesting that there might be an error in the earlier terms.
### Step 5: Check the Sequence
Let's check the multiplication and subtraction pattern as described in the video:
- Starting from 2:
- \(2 \times 2 - 0 = 4\) (should be 4, but we have 6)
- \(4 + 2 = 6\) (this is where the error occurs)
- Continuing:
- \(6 \times 2 - 1 = 11\) (should be 10, but we have 10)
- \(10 \times 2 - 2 = 18\) (should be 19, but we have 19)
- \(19 \times 2 - 3 = 35\) (should be 36, but we have 36)
- \(36 \times 2 - 4 = 68\) (should be 69, but we have 69)
- \(69 \times 2 - 5 = 133\) (should be 134, but we have 134)
### Conclusion
The pattern indicates that the first term after 2 should be 4 instead of 6. Therefore, the wrong number in the series is **6**.
