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?

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==7

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

median==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:

Where is the first term of the set and is the last.

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

mean=.

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

3000 text messages can be sent without breaking the budget.

Step-by-step explanation:

Since each month your cell phone company charges $ 50 for your plan plus 3 cents for each text you send, and you have $ 140 budgeted for cell phone expenses for the month, to make a determination about the number of texts you can send each month the following calculation must be performed:

(140 - 50) / 0.03 = X

90 / 0.03 = X

3000 = X

Therefore, 3000 text messages can be sent without breaking the budget.