Valéria joins a social networking website. After 1 week she has 34 online friends, and after 9 weeks she has 80 online friends.
(1) Find the average number of online friends Valéria has made each week from week 1 to week 9.
(2) Assuming that her total number of online friends after n weeks forms an arithmetic sequence, find a model which approximates the number of online friends after n weeks.
(3) Do you think it is a problem that the common difference in your model is not an integer? Explain your answer.
(4) Use your model to predict how many online friends Valéria will have after 20 weeks.