Question

The first term of set R is 15. What is the median value of the set R, if for every term in the set, Rn = Rn–1 + 3?

Answer 1

Answer:

$median=mean=\frac{R_{n-1}}{2}+9$

Step-by-step explanation:

The first thing to identify is that this one is a consecutive set, meaning that the increment between each number is the same, in this case, an increment of 3 between each number, when sets have this type of behavior, and only on these cases, the mean and the median are the same, let's look at some examples:

[2, 4, 6, 8, 10, 12]

The mean would be:

mean=$\frac{2+4+6+8+10+12}{6}$=7

Since the number of elements is even, the median would be the average of the two middle terms:

median=$\frac{6+8}{2}$=7

As you can see mean=median

There is one more thing to help you in this exercise, for consecutive sets, the mean can also be calculated by the formula:

$mean=\frac{x_{1} + x_{n} }{2}$

Where $x_{1}$ is the first term of the set and $x_{n}$ is the last.

If we ran this formula with the set i used as an example:

mean=$\frac{2+12}{2}=7$.

So applying all of that to the set given we would have:

$median=mean=\frac{15+R_{n-1}+3}{2} =\frac{R_{n-1}+18}{2} =\frac{R_{n-1}}{2}+9$