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 R = 5Q – 20, then find the value of R.

The correct answer is 5.

To find the value of $R$, we first need to determine the value of the variable $Q$ from the table. Let us analyze the sequence formed by the values listed in the "NUMBERS" column of the table:

1st term: $Q$
2nd term: $2.5$
3rd term: $Q-2.5$
4th term: $P$
5th term: $\frac{4Q-5}{2}$
6th term: $18.75$

By observing the relationship between the terms, we can see that they form a multiplication series where each term is obtained by multiplying the preceding term by a factor that increases by $0.5$ at each step:
$\text{Term}\left(n\right)=\text{Term}(n-1)\times [0.5+(n-2)\times 0.5]$

Specifically:
• 2nd term = 1st term $\times 0.5\Rightarrow 2.5=Q\times 0.5$
• Solving for $Q$:
$Q=\frac{2.5}{0.5}=5$

Let us verify the value $Q=5$ by checking the remaining terms in the sequence:
• 1st term = $5$
• 2nd term = $5\times 0.5=2.5$
• 3rd term = $Q-2.5=5-2.5=2.5$ (which is $2.5\times 1.0=2.5$)
• 4th term ($P$) = $2.5\times 1.5=3.75$
• 5th term = $\frac{4\left(5\right)-5}{2}=\frac{15}{2}=7.5$ (which matches $3.75\times 2.0=7.5$)
• 6th term = $7.5\times 2.5=18.75$ (which matches the table value of $18.75$)

The sequence is consistent, validating that $Q=5$.

Now, we substitute $Q=5$ into the equation for $R$:
$R=5Q-20$
$R=5\left(5\right)-20$
$R=25-20$
$R=5$