Directions (55-57): Read the following table carefully and answer the questions given below.

In the table some numbers are given and the probability of picking that number is given.

NUMBERS	Probability
Q	$\frac{1}{6}$
2.5	$\frac{1}{3}$
Q − 2.5	$\frac{1}{3}$
P	$\frac{1}{6}$
$\frac{4Q-5}{2}$	$\frac{1}{6}$
18.75	$\frac{1}{6}$

If the series ‘Q,  2.5,  Q − 2.5,  P,  $\frac{4Q-5}{2}$,  18.75’  follows a certain pattern, then find the value of P.

To find the value of $P$, we need to determine the mathematical pattern followed by the given sequence:
$Q,2.5,Q-2.5,P,\frac{4Q-5,}{2},18.75$

Let us examine the relationship between consecutive terms. Let the terms of the series be denoted by
$a_1=Q$
$a_2=2.5$
$a_3=Q-2.5$
$a_4=P$
$a_5=\frac{4Q-5}{2}$
$a_6=18.75$

Let's test a multiplication-addition/subtraction pattern. Specifically, let's assume each term is obtained by multiplying the previous term by a factor that increases or decreases, and adding/subtracting a value.
Let's consider the relation between the first three terms:
If $a_2=a_1\times 1-2.5$, then $2.5=Q-2.5\Rightarrow Q=5$.

Let us check if $Q=5$ makes the sequence consistent:
If $Q=5$, the terms become:
$a_1=5$
$a_2=2.5$
$a_3=5-2.5=2.5$
$a_5=\frac{4\left(5\right)-5}{2}=\frac{15}{2}=7.5$
$a_6=18.75$

Now let's find the pattern for the sequence $5,2.5,2.5,P,7.5,18.75$:
1. $a_2=a_1\times 0.5=5\times 0.5=2.5$
2. $a_3=a_2\times 1.0=2.5\times 1=2.5$
3. $a_4=a_3\times 1.5=2.5\times 1.5=3.75$
4. $a_5=a_4\times 2.0=3.75\times 2=7.5$
5. $a_6=a_5\times 2.5=7.5\times 2.5=18.75$

The pattern perfectly holds for all terms, where each term is multiplied by a multiplier that increases by $0.5$ at each step ($\times 0.5,\times 1,\times 1.5,\times 2,\times 2.5$).
Therefore, the value of $P$ is:
$P=3.75$