The phrase "appears to be methodically" is correct and usable in written English.
You can use it when describing a process or action that seems to be carried out in a systematic or organized manner.
Example: "The research team appears to be methodically analyzing the data to ensure accurate results."
Alternatives: "seems to be systematically" or "looks to be organized in a methodical way."
States are methodically creating and expanding programs to help low-income elderly people buy prescription drugs, even as Congress appears to be floundering in efforts to add drug benefits to Medicare.
If progress can be measured in hours spent in conference rooms, then the N.B.A. lockout would appear to be moving — slowly, methodically — toward some sort of conclusion.
Throughout the primaries, Romney had appeared to be the only Republican running a 21st-century campaign, methodically banking early votes in states like Florida and Ohio before his disorganized opponents could establish operations there.
The man, who appeared to be in his 40s, first sprays the woman in the face, then douses her methodically from head to toe with what a city official said was an accelerant as she turned and cowered, raising her hands, the grocery bags hanging from her wrists.
They are questions that not only citizens, but government itself needs to be methodically asking.
Regarding this overview, healthful products should be methodically designed to encourage consumers to choose a fat-replaced product.
This type of research must be methodically planned and implemented with attention to validity, reliability, and relevance.
According to Newt Gingrich, Mr. Romney is "methodically dishonest" and "lives in a world of Swiss bank accounts, Cayman Island accounts".
A video released Thursday appears to show Islamic State militants methodically destroying centuries-old artifacts in the northern Iraqi city of Mosul, which would be the group's most brazen attack to date on antiquities regarded by the extremists as idolatrous.
