I know this discussion is getting too deep for me and I don't dare jump off the boat without my life vest for I will drown.
So I will play in the shallow waters by myself and answer the title of the thread in as short of a sentence as possible:
;repent and believe the gospel!
Halleluyah y'all!
I know you are probably referring to Acts 2:38 in that altar call to the Jews, but what does repent to you mean when that same Peter gave this altar call to the Gentiles where the word repent was not used, but to believe in Jesus Christ for the remission of sins and they obviously believed Peters words and got the Holy Ghost and before water baptism too.
Acts 10:43 To him give all the prophets witness, that through his name whosoever believeth in him shall receive remission of sins.
44 While Peter yet spake these words, the Holy Ghost fell on all them which heard the word.
45 And they of the circumcision which believed were astonished, as many as came with Peter, because that on the Gentiles also was poured out the gift of the Holy Ghost.
46 For they heard them speak with tongues, and magnify God. Then answered Peter,
47 Can any man forbid water, that these should not be baptized
, which have received the Holy Ghost as well as we?
48 And he commanded them to be baptized in the name of the Lord. Then prayed they him to tarry certain days.
So the Jews testified they had received the Holy Ghost same as the Gentiles and so this same Peter preached the same gospel for why discernment is needed to know what the Jews repented of because Peter did not say the words of believing in Him for the remission of sins, but that is what Peter ad meant when he had said repent when we read in context of what it was the Jews were pricked in their hearts for to repent of, crucifying Jesus in unbelief for blasphemy, as claiming to be God was what He was crucified for.
Acts 2:36 Therefore let all the house of Israel know assuredly, that God hath made the same Jesus, whom ye have crucified, both Lord and Christ.
37 Now when they heard this, they were pricked in their heart, and said unto Peter and to the rest of the apostles, Men and brethren, what shall we do?
38 Then Peter said unto them, Repent, and be baptized every one of you in the name of Jesus Christ for the remission of sins, and ye shall receive the gift of the Holy Ghost.
So "Repent" here is repent from unbelief by believing in Him in order to get the remissions of sins and the gift of the Holy Ghost as same as the Gentiles.
Naysayers cannot answer why Peter did not say believe in Him for the remission of sins to the Jews and yet that is what Peter said to the Gentiles nor why Peter did not say repent to the Gentiles when all he said was to believe in Him for the remission of sins and they got the Holy Ghost, but yet Peter had said that to the Jews. Same message, and same gospel, but many reader and believers are overlooking what repent meant to the Jews as repenting from unbelief.
I hope the Lord is ministering and that you may find this reply not so in the deep end as you may think it is. May God cause the increase on how we are saved by believing in Jesus Christ for eternal life.