It took a lot less code to do the first problem in F#:

let problem1 =
    [1 .. 999]
    |> Seq.filter (fun x -> x % 3 = 0 || x % 5 = 0)
    |> Seq.fold (+) 0

printfn "The sum of all multiples of 3 and 5 below 1000 is %d" problem1