"Seeking for an answer" or "seeking an answer"
Solution 1:
'For' is implied by 'seeking' and therefore redundant.
In 'searching an answer,' 'for' is not implied and should be added.
One of those English mysteries, I guess.
Solution 2:
'Seeking an answer' since 'seeking ' means 'looking for'.
Solution 3:
This is covered in this good dictionary
Cambridge Advanced Learner's Dictionary
Remember: Seek is not usually followed by a preposition.
NOT: I went to the beach seeking for peace and fresh air.
Correct: I went to the beach seeking peace and fresh air.