Note something of considerable importance to church members: Both Isaiah and Amos addressed their counsel to people who had already made a covenant with God. Why? Because these Israelites were in serious spiritual trouble within the relationship that the covenant created. These are stern exhortations for them to get on the ball.
A second but not readily apparent reason why these warnings are important to us is that seeking after God truly does not begin until after He reveals Himself to us and we make the covenant with Him. Many do not realize that seeking God is the main occupation for a Christian during the sanctification process. Amos is clear regarding this.
God warns how devastating the coming perilous times will be, then He counsels us to seek the help of One far greater - our Creator and Ruler. Finally, He urges us to turn our everyday conduct to seeking to do good, showing care for God and His people.
Amos is not charging the Israelites to seek God in order to find Him because, at the very least, they were acquainted with Him, having already made the covenant with Him. However, that He charges them with seeking Him reveals that despite making the covenant, what they knew about Him had not been translated into everyday living or being like Him. This indicates that they were just drifting along with the times.
Four times in Amos 5, he urges them to seek God, and two of those times, he adds, "that you may live." This thought ties directly into John 17:3, which indicates that, more than being just endless existence, eternal life is a quality of life. As we proceed, we will see that they were being exhorted to seek God because, despite having made the covenant, they had stopped seeking Him, and the effect of stopping was their poor spiritual condition and subsequently, their imminent destruction at the hand of the Assyrians.