The choice that correctly identifies the type of verb traveling is in each of the sentence above is option A. Sentence 1: gerund, sentence 2: participle.
Sentence 1 uses the word "Traveling" as a gerund. A gerund is a word that takes the verb form -ing, but functions as a noun in the sentence. In sentence 2, the word "traveling" is used as a participle. A participle is a word that also takes the form of a verb, but functions as an adjective or as a noun.