This information can easily be obtained, but the notation that I am using is different. I am looking at the number of trials (k) it takes to obtain r successes, given a certain probability p. This is in contrast to the notation used in Wikipedia, that uses the notation as r failures in k trials.
I also cannot find the information in the textbook.
Hint:
We can write $X=X_1+\cdots+X_r$ where the $X_i$ are iid having geometric distribution with parameter $p$.
Here e.g. $X_i$ counts the number of trials needed to arrive at the first success. Then $X_2$ counts the number of trials (after reaching the first success) needed to arrive at the second success. Et cetera.
Apply linearity of expectation and note that the independence of the $X_i$ also implies linearity when it comes to variance.