The question asks us to find the number that replaces the question mark (?) in the given number series: 14, 2, 28, 3, 84, 4, ?

Identifying the Series Pattern

Let's analyze the relationship between the numbers in the series. We can observe a pattern by looking at terms separated by one position:

• The 1st term is 14.
• The 2nd term is 2.
• The 3rd term (28) relates to the 1st term (14). The operation is: 14 × 2 = 28.
• The 4th term (3) relates to the 2nd term (2). The operation is: 2 + 1 = 3.
• The 5th term (84) relates to the 3rd term (28). The operation is: 28 × 3 = 84.
• The 6th term (4) relates to the 4th term (3). The operation is: 3 + 1 = 4.

The pattern involves two alternating operations:

1. Multiplying the term at position $n$ by $(n/2 + 1)$ to get the term at position $n+2$ (for odd $n$, starting from $n=1$). Specifically, the multipliers are 2, 3, 4...
2. Adding 1 to the term at position $n$ to get the term at position $n+2$ (for even $n$, starting from $n=2$). The constant addition is +1.

Calculating the Missing Term

Following the established pattern, the 7th term (?) should be calculated based on the 5th term (84) using the next multiplier in the sequence.

• The multiplier sequence is 2, 3, 4. The next multiplier is 4.
• The calculation is: 5th term × 4
• So, ? = 84 × 4

Performing the calculation:

$ 84 \times 4 = 336 $

Therefore, the number that replaces the question mark is 336.

Final Answer

The missing number in the series is 336, which corresponds to Option C.