Find the wrong number in the following series :
69, 55, 26, 13, 5

Question

Find the wrong number in the following series : 
69, 55, 26, 13, 5

Accepted Answer

The series given is: 69, 55, 26, 13, 5.

To determine the wrong number in the series, we need to identify a pattern or rule that applies to the majority of the numbers. Let's analyze the series:

1. **Difference between consecutive numbers:**
   - 69 - 55 = 14
   - 55 - 26 = 29
   - 26 - 13 = 13
   - 13 - 5 = 8

The differences between consecutive numbers do not follow a consistent pattern, which suggests that one of the numbers might be incorrect.

2. **Analyzing the pattern:**
   - If we observe the series, it seems to be decreasing, but the differences are not consistent. Let's try to find a logical pattern:
   - The series could potentially be based on a pattern where each number is derived from a specific operation on the previous number.

3. **Identifying the wrong number:**
   - If we assume a pattern where each number is derived by subtracting a certain value from the previous number, we can test this hypothesis:
   - Starting from 69, if we subtract 14, we get 55.
   - From 55, if we subtract 29, we get 26.
   - From 26, if we subtract 13, we get 13.
   - From 13, if we subtract 8, we get 5.

However, the differences (14, 29, 13, 8) do not form a consistent pattern, indicating that one of these numbers is incorrect.

4. **Justifying why 5 is the wrong number:**
   - The series appears to be decreasing, but the final difference (13 - 5 = 8) does not fit with any logical pattern derived from the previous differences.
   - If we consider the possibility of a consistent pattern, the number 5 does not fit well with the rest of the series, as it disrupts any potential arithmetic or geometric progression.

5. **Why the other options are incorrect:**
   - **Option 2 (13):** The number 13 fits well after 26, as the difference (26 - 13 = 13) is a plausible step in a decreasing series.
   - **Option 3 (26):** The number 26 follows logically after 55, with a difference of 29, which could be part of a decreasing pattern.
   - **Option 4 (55):** The number 55 follows logically after 69, with a difference of 14, which is a reasonable step in a decreasing series.

In conclusion, the number 5 is the wrong number in the series because it does not fit any consistent pattern or logical progression derived from the other numbers. Therefore, Option 1 is the correct answer.