Series Pattern Analysis: Finding the Missing Term

The question presents a number series: 7, 3, 6, 7, 5, 11, ? and asks to find the term that replaces the question mark. To solve this, we need to identify the underlying pattern governing the sequence.

Identifying the Interleaved Series Pattern

Upon closer inspection, the series does not follow a single, simple arithmetic or geometric progression. However, it can be observed that the series consists of two separate, interleaved patterns:

• Terms at odd positions (1st, 3rd, 5th, 7th, ...).
• Terms at even positions (2nd, 4th, 6th, ...).

Analyzing the Odd Position Series

Let's look at the terms in the odd positions:

• 1st term: 7
• 3rd term: 6
• 5th term: 5

The pattern here is that each term is 1 less than the previous term in this sub-series (7, 6, 5, ...). This is an arithmetic progression with a common difference of -1.

Following this pattern, the next term in the odd position series (which would be the 7th term overall) should be $5 - 1 = 4$.

Analyzing the Even Position Series

Now, let's examine the terms in the even positions:

• 2nd term: 3
• 4th term: 7
• 6th term: 11

The pattern here is that each term is 4 more than the previous term in this sub-series (3, 7, 11, ...). This is an arithmetic progression with a common difference of +4.

The next term in this sub-series (which would be the 8th term overall) would be $11 + 4 = 15$.

Determining the Missing Term

The question mark is located at the 7th position in the original series. As established, the 7th position belongs to the series of odd-positioned terms.

Based on the pattern identified for the odd positions (7, 6, 5, ...), the 7th term is calculated as $5 - 1 = 4$.

Therefore, the number that replaces the question mark is 4.