I understand that you want your code to look like C #. But F # is a functional language (not strictly, but that basic paradigm), and in these features lies the power of the language. First create your collection. A more idiomatic type is the List. It is unchanged, which is one of the functional features of the language.
let words = ["how"; "are"; "you"]
Since it is immutable, you expand it by creating a new collection. You can add an element at the beginning:
let moreWords = "Hello" :: words
or join one list with another:
let evenMore = moreWords @ ["I"; "am"; "fine"]
Then iteration. For a cycle is a purely imperative construct. Since we switched to the functional collection, use one of the built-in List functions to iterate:
let prnt lst = lst |> List.iter (fun x -> printfn "%s" x)
It will take a list. Iterates over each element. And it executes a function (fun x -> printfn "%s" x) for each element.
Or you can play a little and write your own function to go through all the elements and execute a function for each of them. One approach is to use recursion and list matching:
let rec loopFn lst fn = match lst with | [] -> fn | head::tail -> fn head loopFn tail fn
This funciton takes a list and another function as arguments. Matches the list. If it is empty ( | [] ) - performs a function. Otherwise, the list is divided into heads, and the rest ( head::tail ) performs the function in head ( fn head ) and then on the remaining elements ( loopFn tail fn ).
To print items, go to the function in the word list and the print function:
loopFn words (fun x -> printfn "%s" x)
or since printfn is the function itself, you can simplify the call a bit:
loopFn words (printfn "%s")