Pattern Analysis:
To find the missing number in the sequence, we need to identify the pattern or rule that governs the sequence. Let's analyze the given sequence:

4, 5, 6, 14, ?, 100.5

First Difference:
The first difference between consecutive terms in the sequence is:

5 - 4 = 1
6 - 5 = 1
14 - 6 = 8

The first difference increases by 7 each time.

Second Difference:
Now let's calculate the second difference between consecutive terms:

1 - 1 = 0
8 - 1 = 7

The second difference remains constant at 7.

Pattern Analysis:
Based on the analysis of the differences, we can determine that the sequence follows a quadratic pattern, where the second difference is constant. Let's express the sequence as a quadratic equation:

a(n) = An^2 + Bn + C

where n is the position of the term in the sequence.

Identifying the Quadratic Equation:
To find the quadratic equation that represents the sequence, we can substitute the first three terms into the equation:

A(1)^2 + B(1) + C = 4
A(2)^2 + B(2) + C = 5
A(3)^2 + B(3) + C = 6

Simplifying these equations, we get:

A + B + C = 4 ...(1)
4A + 2B + C = 5 ...(2)
9A + 3B + C = 6 ...(3)

Solving these equations simultaneously, we find:
A = 1/2
B = 3/2
C = 2

Therefore, the quadratic equation that represents the sequence is:
a(n) = (1/2)n^2 + (3/2)n + 2

Calculating the Missing Term:
Now, let's substitute the position of the missing term, which is 5, into the equation to find its value:

a(5) = (1/2)(5)^2 + (3/2)(5) + 2
= (1/2)(25) + (15/2) + 2
= 12.5 + 7.5 + 2
= 22

Therefore, the missing term in the sequence is 22.

Conclusion:
The missing term in the sequence 4, 5, 6, 14, ?, 100.5 is 22. The correct answer is option 'A' (32.5)