There has only been one Swedish king called Fredrik. Fredrik I, married to Queen Ulrika Eleonora, who inherited the throne after the death of King Charles XII. Ulrika abdicated in favour of Fredrik. [noted -ed]
There was however, a Swedish king named Adolf Fredrik (he went by both names). He lived 1710-1771 and became king 1751. He succeeded Fredrik I and was himself succeded by his son, Gustav III.