If a person has led a sinful life and has been instrumental in causing others to sin, would it be possible for such a one to be fully forgiven and all their past sins cancelled if they should repent and ask the Lord to forgive them?

There should be no question in the mind of any one on this point. The Scriptures abound with expressions in which the Divine love and compassion of God, the Heavenly Father, are declared. The great Creator of the Universe sacrificed His beloved son, the Lord Jesus Christ, to redeem the world and to reconcile it to Himself. Those, therefore, who will accept the Lord Jesus as their Savior, and believe that he by the grace of God tasted death for every man (Hebrews 2:9) – these are freely forgiven all their past iniquities. 

Before his conversion to Christianity, the Apostle Paul was bitterly opposed to the cause of Christ. He went about persecuting the followers of the Master. He put them in prison and arranged that some should be put to death. We remember that he consented to the death of Stephen, the first martyr (Acts 7:58,59). Yet with all this, the Lord freely forgave him. Note the following Scriptures as evidencing the full and complete forgiveness of all those who are truly repentant and who desire to draw nigh to God through Christ (Isaiah 1:18; Psalms 103:10-14; Acts 26:18; Ephesians 1:7; Colossians 1:14).

Additional Resource:
Christian Questions Podcast
Episode #935: “Does God Really Forgive Me?”
How our forgiveness from God and for each other works
Preview Video
CQ Rewind Show Notes

Episode #1289: “How Do I Know If I Have Really Forgiven Someone?”
The depth, power and appropriate applications of true forgiveness
Preview Video
CQ Rewind Show Notes 

For children, parents and Bible class teachers:
Animated video: Why should we forgive others?