Each of the gospels have a specific goal or objective in writing their message, but they all basically agree in their testimony about Christ. Matthew writes to prove that Jesus is the Messiah of the Jews. But in his gospel, he speaks of faith and forgiveness of sin (cf. Matt. 9:1f; see also 26:28).
Luke, a Gentile himself, writes to prove who Jesus is as the Son of Man, but also as the one who came seeking to save that which was lost (Luke 19:10). Mark, the shortest of the Gospels, also writes to Gentiles, but more specifically, to the Romans, a people of action and few words, to show that Jesus is the Servant of the Lord, the One who came not to be ministered to, but to give his life a ransom (a payment for sin) for many (Mark 10:45). In Mark, Christ is the serving, sacrificing Savior. Luke is also the author of the book of Acts which repeatedly mentions the need of faith in Christ. In each of these gospels, however, the emphasis is more on discipleship and what discipleship requires. But inherent in each of their messages is the need of faith in Jesus because they are writing to prove who He really is and what He accomplished because each gospel ends with the resurrection.
John, on the other hand, specifically states his purpose is to lead people to believe in Christ as Savior. Compare John 20:30f. Thus, the word “believe” in one form or another is mentioned some 95 times. His purpose was different from the others, but he was also one of the original disciples and one of the apostles. Matthew, Mark, and Luke all use the word “repent” in relation to salvation (Matt. 3:2; 4:17; Mark 1:15; 6:12; Luke 13:3-5; 16:30). The question is, what does repent mean? The word really means to change your mind and is a synonym, in some contexts, for believing. In a context dealing with salvation from sin, it carries the idea of turning from one’s false sources of trust, like the external religion of the Pharisees (see Matt. 5:20), or no trust at all, to faith in the person and work of Christ as the Messiah of the Old Testament, which included a suffering Savior who would bear our sin (see Isa. 52:12-53:1f).