Christians serve God BECAUSE they’ve been saved… not IN ORDER TO be saved.  Consider Deuteronomy 10:21-11:1…

He (God) is your praise.  He is your God, who has done for you these great and terrifying things that your eyes have seen. 22 Your fathers went down to Egypt seventy persons, and now the LORD your God has made you as numerous as the stars of heaven.  11:1 You shall therefore love the LORD your God and keep His charge, His statutes, His rules, and His commandments always.

The same is found in Exodus 19:3-6…

The LORD called to (Moses) out of the mountain, saying, “Thus you shall say to the house of Jacob, and tell the people of Israel: 4 You yourselves have seen what I did to the Egyptians, and how I bore you on eagles’ wings and brought you to myself. 5 Now therefore, if you will indeed obey my voice and keep my covenant, you shall be my treasured possession among all peoples, for all the earth is mine;  6 and you shall be to me akingdom of priests and a holy nation. These are the words that you shall speak to the people of Israel.”

It is worth noting that the Ten Commandments were given AFTER the Children of Israel were delivered from Egypt.  That is important because it points to the truth that deliverance comes BEFORE obedience… both for the Children of Israel AND believers today.  To put it another way is… deliverance brings about obedience to God.

The New Testament way this is set forth is found in Ephesians 2:8-10…

For by grace you have been saved through faith. And this is not your own doing; it is the gift of God, 9 not a result of works, so that no one may boast.  10 For we are his workmanship, created in Christ Jesus for good works, which God prepared beforehand, that we should walk in them.

Again, salvation is a gift from God.  Salvation is deliverance from sin, which the Exodus pictured in the books of Exodus and Deuteronomy.  Works are the sign that a person has been delivered, not the means by which they are delivered from sin.

We serve God because He is God.  We serve God because He is good.  We serve God because our service brings glory to His name.  We serve God because there is nothing higher or better we can do in this life!  We do not serve God in order to be saved… that is heretical and impossible.