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

6, 8, 12, 42, 160, ?

- The difference between the first two numbers is 8 - 6 = 2.
- The difference between the second and third numbers is 12 - 8 = 4.
- The difference between the third and fourth numbers is 42 - 12 = 30.
- The difference between the fourth and fifth numbers is 160 - 42 = 118.

From the given differences, we can observe that the differences between the numbers are not constant, indicating that a simple arithmetic progression is not followed.

Quadratic Pattern:
Upon further analysis, the differences between the numbers seem to be increasing. Let's examine the differences between the differences:

4 - 2 = 2
30 - 4 = 26
118 - 30 = 88

The differences between the differences (second differences) are not constant either. However, if we look at the pattern closely, we can see that the second differences are increasing by a constant value. This suggests that the sequence might follow a quadratic pattern.

Let's assume that the sequence follows a quadratic equation of the form:
an² + bn + c

Using the given numbers, we can form three equations to solve for the coefficients a, b, and c:

Equation 1: 1²a + 1b + c = 6
Equation 2: 2²a + 2b + c = 8
Equation 3: 3²a + 3b + c = 12

Solving these equations simultaneously, we get:
a = 1/2, b = 5/2, c = 4

Now, we can substitute the values of a, b, and c into the quadratic equation to find the missing number:

6, 8, 12, 42, 160, ?

Substituting n = 5 into the quadratic equation:
5²(1/2) + 5(5/2) + 4 = 25/2 + 25/2 + 4 = 12.5 + 12.5 + 4 = 29

Therefore, the missing number in the sequence is 29.

Answer Explanation:
The correct answer is option 'D' (810), which is not mentioned in the question. The given options are irrelevant to the pattern analysis of the sequence, making them incorrect.