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 \(T_{n-1} + T_{n-2}\).

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 \(64\).