Find the wrong number in the given series. 4, 8, 16, 24, 40, 62, 104, 168, 296
62
Number Series Analysis
To identify the wrong number in the given series, we need to carefully analyze the pattern followed by the numbers. The given number series is:
\(4, 8, 16, 24, 40, 62, 104, 168, 296\)
Identifying the Series Pattern
Let's examine the relationship between consecutive terms to find a consistent logical pattern. Often, in such number series questions, a pattern involves addition, subtraction, multiplication, division, or a combination of these operations, sometimes referring to previous terms.
Consider a common pattern where a term is the sum of its two preceding terms, similar to a Fibonacci series, but with a specific starting point:
- The first term is \(T_1 = 4\)
- The second term is \(T_2 = 8\)
- The third term is \(T_3 = 16\)
Now, let's test the hypothesis that from the fourth term onwards, each number is the sum of its two preceding numbers. That is, for \(n \ge 4\), the term \(T_n\) should be equal to \(T_{n-1} + T_{n-2}\).
| Term Number | Given Term | Expected Pattern \(T_n = T_{n-1} + T_{n-2}\) | Observation |
|---|---|---|---|
| \(T_1\) | \(4\) | \(-\) | Starting term |
| \(T_2\) | \(8\) | \(-\) | Starting term |
| \(T_3\) | \(16\) | \(-\) | Starting term |
| \(T_4\) | \(24\) | \(T_3 + T_2 = 16 + 8 = 24\) | Matches the given number. |
| \(T_5\) | \(40\) | \(T_4 + T_3 = 24 + 16 = 40\) | Matches the given number. |
| \(T_6\) | \(62\) | \(T_5 + T_4 = 40 + 24 = 64\) | Does NOT match the given number \(62\). The expected number is \(64\). |
| \(T_7\) | \(104\) | If \(T_6\) was \(64\): \(T_6 + T_5 = 64 + 40 = 104\) | Matches the given number. This confirms \(62\) is the wrong number if the pattern is to continue correctly. |
| \(T_8\) | \(168\) | If \(T_6\) was \(64\): \(T_7 + T_6 = 104 + 64 = 168\) | Matches the given number. |
| \(T_9\) | \(296\) | If \(T_6\) was \(64\): \(T_8 + T_7 = 168 + 104 = 272\) | Does NOT match the given number \(296\). However, in "find the wrong number" questions, typically only one prominent error needs to be identified. The error at \(T_6\) is the first and most direct break in the established pattern that then allows subsequent numbers to match if corrected. |
Identifying the Wrong Number
Based on our analysis, the pattern where each term is the sum of the two preceding terms starts consistently from \(T_4\).
- The sequence correctly follows this pattern up to \(T_5\).
- For \(T_6\), the expected value based on the pattern \(T_5 + T_4\) is \(40 + 24 = 64\).
- However, the given series has \(62\) at this position.
- If \(62\) is corrected to \(64\), then the subsequent terms, \(104\) (\(40 + 64\)) and \(168\) (\(64 + 104\)), fit the pattern perfectly.
Therefore, \(62\) is the wrong number in the given series as it disrupts the established additive pattern.
The correct number in place of \(62\) should be \(64\).
Important Questions from Reasoning
Four words have been given, out of which three are alike in some manner and one is different. Select the one that is different.
Ramesh went 15 m to the east, then he turned left and after \(5\sqrt 3 \) m turned 120° right and went \(10\sqrt 3 \) m and then turned 120° right and went \(20\sqrt 3 \) m. How far was Ramesh from the starting point ?
Select the missing number from the given responses.
5 6 3 8 9 6 8 7 7 4 5 6 51 38 29 ? Arrange the following words according to the English Dictionary :
1. Appropriate
2. Appreciate
3. Appearance
4. Application
5. Applaud
Select the one which is different from the other three responses.
