Forgiven to serve is a gift from the Lord. Romans 6:23 For the wages of sin is death, but the free gift of God is eternal life through Christ Jesus our Lord.  As a youth, I understood in child-like faith what Jesus did for me, but I was an adult before I began to grasp the depth of what Jesus did for me on the cross.
When we meditate on what Jesus did for each of us on the cross, we begin to realize what an incredible gift forgiveness is. Without the forgiveness Jesus paid for with His blood on the cross, we would not have hope of eternal life or anything beyond this world. The Lord saves us not so we can go our own way but to fulfill the Lord’s plans for our life.
Jesus Forgave Peter
Jesus warned Peter that he would deny Him, and he insisted that would never happen. A few hours later, Peter denied him just as He said he would. Luke 22:61 At that moment the Lord turned and looked at Peter. Suddenly, the Lord’s words flashed through Peter’s mind: “Before the rooster crows tomorrow morning, you will deny three times that you even know me.” 62 And Peter left the courtyard, weeping bitterly. 
Peter boasted about his bravery in standing for Jesus, but when the time came, he failed. Only John would be at the cross when Jesus was crucified while Peter and the others ran and hid. Denying Jesus was a humbling experience for Peter, but he would be restored. After Jesus’ resurrection, he came to the disciples who were fishing.
Jesus Restored Peter
John 21:15 After breakfast, Jesus asked Simon Peter, “Simon, son of John, do you love me more than these?” “Yes, Lord,” Peter replied, “you know I love you.”  Three times Jesus asked Peter if he loved him, and Peter responded three times that he loved Him like a brother. Jesus knew Peter’s love for Him would grow over time from brotherly love to sacrificial love. John 21:19 Then Jesus told him, “Follow me.”
Jesus forgave and restored Peter and called him a second time to come and follow Him. Peter would grow in faith through this situation and powerfully serve Jesus throughout his life. Like Peter, we are forgiven not to serve ourselves but to serve Jesus as we do His work.
Paul tells us about the connection between forgiveness, salvation, and serving. Ephesians 2:8 God saved you by his grace when you believed. And you can’t take credit for this; it is a gift from God. 9 Salvation is not a reward for the good things we have done, so none of us can boast about it. 10 For we are God’s masterpiece. He has created us anew in Christ Jesus, so we can do the good things he planned for us long ago. 
To hear how we are forgiven to serve, listen here:
[1-5] Tyndale House Publishers. (2015). Holy Bible: New Living Translation. Tyndale House Publishers.