To find the wrong number in the series 7, 23, 58, 127, 269, 555, we will analyze the pattern step by step.
### Step 1: Identify the pattern
We notice that each number seems to be related to the previous number by doubling it and then adding an odd number. Let's check this hypothesis.
### Step 2: Calculate the differences
1. Start with the first number: **7**
- Double it: \( 7 \times 2 = 14 \)
- To get to the next number (23), we need to add \( 23 - 14 = 9 \).
So, \( 7 \times 2 + 9 = 23 \).
2. Next, take **23**:
- Double it: \( 23 \times 2 = 46 \)
- To get to the next number (58), we need to add \( 58 - 46 = 12 \).
So, \( 23 \times 2 + 12 = 58 \).
3. Now, take **58**:
- Double it: \( 58 \times 2 = 116 \)
- To get to the next number (127), we need to add \( 127 - 116 = 11 \).
So, \( 58 \times 2 + 11 = 127 \).
4. Next, take **127**:
- Double it: \( 127 \times 2 = 254 \)
- To get to the next number (269), we need to add \( 269 - 254 = 15 \).
So, \( 127 \times 2 + 15 = 269 \).
5. Finally, take **269**:
- Double it: \( 269 \times 2 = 538 \)
- To get to the next number (555), we need to add \( 555 - 538 = 17 \).
So, \( 269 \times 2 + 17 = 555 \).
### Step 3: Analyze the odd numbers added
The odd numbers added are:
- From 7 to 23: **9**
- From 23 to 58: **12**
- From 58 to 127: **11**
- From 127 to 269: **15**
- From 269 to 555: **17**
### Step 4: Identify the inconsistency
The odd numbers added do not follow a consistent pattern. The sequence of odd numbers should ideally be increasing. The sequence of added odd numbers is:
- 9, 12, 11, 15, 17
Notice that after 9, we should have 11, then 13, but we have 12 instead. This indicates that **58** is the wrong number.
### Step 5: Correct the wrong number
If we replace **58** with **57**:
- From 23 to 57: \( 23 \times 2 + 11 = 57 \)
- From 57 to 127: \( 57 \times 2 + 13 = 127 \)
This maintains the pattern of adding increasing odd numbers.
### Conclusion
The wrong number in the series is **58**, and it should be replaced with **57**.
