There are 9 consecutive integers in a certain sequence. If the average

USEFUL RULE: In a set of EQUALLY SPACED numbers, the mean of the set equals the median of the set

Let O, O, O, O, O, O, O, O, O represent the 9 consecutive integers listed in ascending order.

The average (aka MEAN) of the first seven integers in the sequence is n
Here are the first seven integers: O, O, O, O, O, O, O
Since consecutive integers are equally spaced, the mean = the median
The median of these 7 numbers is the middlemost number.
So, the middlemost value is also the mean.
We get: O, O, O, n, O, O, O
So, our NINE numbers now look like this: O, O, O, n, O, O, O, O, O

What is the average of all 9 integers in the sequence?
Using the same logic, we can see that the mean of the 9 numbers is the middlemost number.
So, replace the middlemost number with a "?" : O, O, O, n, ?, O, O, O, O

We can see that ? (the mean of all 9 integers) is 1 GREATER THAN n (the mean of the first 7 integers)
In other words, the mean of all 9 integers = n+1

Answer: C