[susan53]

1)
Our friendship____________________quickly over the weeks that followed.

Options:
a)had developed b)would develop c)was developing d)developed

Lousy question. Given the correct context, any of them are possible.

a) David was astounded. "You're engaged to Jack!" he said. "But I thought you hated him!" His reaction was justified of course. He had last seen us together when we first met, in that dreadful training course that we'd taken together. But afterwards we had all calmed down, and our friendship had developed quickly over the weeks that followed.

Past perfect = sequences an event as happening before a reference point (the moment of David's reaction)

b) I didn't like Jack when we first met. But our friendship would develop quickly in the weeks that followed, and soon turn into something more.
would = second form of will, indicating a prediction made from a past viewpoint

c) I didn't like Jack when we first met. But, over the weeks that followed, it soon became apparent that our friendship was developing quickly.
Past continuous = an ongoing event

d) I didn't like Jack when we first met, but our friendship developed quickly over the weeks that followed, and we soon became firm friends.
Past simple = past finished event.

I had to change the sentence slightly to make (c) sound natural, but the point is, as always, that these 4 verb forms express different meanings - and the speaker will choose the form depending on how s/he sees the event and therefore which meaning s/he wants to express - which will in turn depend largely on the context. Take away the context (as this type of exercise does) and it is nearly always impossible to say if a grammatical form is possible or not.