How can we better understand 1st Peter chapter 1? Read below what I have suggested. Perhaps you could add how you think this Bible study could be improved.
First Peter chapter 1 was written by a man of God who knew full well what the church needed to learn and to hear. He went from being a disciple that denied Christ 3 times to one that boldly proclaimed the gospel to all that would hear, regardless of the consequences, which often resulted in beatings and being cast into jail. I am excited to dive into this chapter and find ways in which we can better understand the Word of God and specifically the first chapter of 1st Peter.
The Begotten Elect
First Peter 1:1-2 “To those who are elect exiles of the Dispersion in Pontus, Galatia, Cappadocia, Asia, and Bithynia, according to the foreknowledge of God the Father, in the sanctification of the Spirit, for obedience to Jesus Christ and for sprinkling with his blood: May grace and peace be multiplied to you.”
It is clear that Peter is writing to the Jews who are dispersed (called the Dispersion) throughout the Roman Empire. He calls them the elect, meaning that God has elected to save those who trust in Christ. This election was like God was the only One Who voted. The final vote was God 1, everyone else 0. That’s because our election was “according to the foreknowledge of God the Father.” The word used for “foreknowledge” is “prognosis” which means “with forethought” or “by pre-arrangement” so we are destined to be saved with God’s forethought, by pre-arrangement even before we were born. You can read more about this in Ephesians  chapter 1. Who do you think these elect were? Do you consider yourself an elect one? What does it mean to have peace and grace multiplied?
Our Kept Inheritance
First Peter 1:3-5 “Blessed be the God and Father of our Lord Jesus Christ! According to his great mercy, he has caused us to be born again to a living hope through the resurrection of Jesus Christ from the dead, to an inheritance that is imperishable, undefiled, and unfading, kept in heaven for you, who by God’s power are being guarded through faith for a salvation ready to be revealed in the last time.”
Imagine you are going to inherit millions of dollars and that inheritance is kept by God Himself. That is the idea behind Peter’s statement that we have an “imperishable, undefiled, and unfading, kept in heaven for” us. Has God really “caused us to be born again” (John 3:3, 5)? What about freewill? I thought we choose to be saved (John 3:16)? What does it mean that God caused us to be born again? How is this imperishable, undefiled, and unfading inheritance kept for us? How is it guarded through faith? Is it our faith or the gift of faith from God that guards it? Why is it not revealed until “the last time?”
Is our Faith Tested by Trials?
First Peter 1:6-9 “In this you rejoice, though now for a little while, if necessary, you have been grieved by various trials, so that the tested genuineness of your faith—more precious than gold that perishes though it is tested by fire—may be found to result in praise and glory and honor at the revelation of Jesus Christ. Though you have not seen him, you love him. Though you do not now see him, you believe in him and rejoice with joy that is inexpressible and filled with glory, obtaining the outcome of your faith, the salvation of your souls.”
It is true that a faith that had not been tested cannot be trusted so what does Peter mean that the “genuineness of [our] faith” will be “tested by fire?” What if we fail this test? Can we fail it? Does Peter mean that “obtaining the outcome of [our] faith” and “the salvation of [our] souls” depends on whether we pass or fail the test? What does he mean by the genuineness of our faith? Can we fake it?
Angels Desire to Look into?
First Peter 1:10-12 “Concerning this salvation, the prophets who prophesied about the grace that was to be yours searched and inquired carefully, inquiring what person or time the Spirit of Christ in them was indicating when he predicted the sufferings of Christ and the subsequent glories. It was revealed to them that they were serving not themselves but you, in the things that have now been announced to you through those who preached the good news to you by the Holy Spirit sent from heaven, things into which angels long to look.”
What does Peter mean by saying that the prophets who prophesied about Christ were “serving not themselves but you” and me? Who revealed this to the prophets that they were not serving themselves but us ? What is it that the angels long to look into? Why are they curious about it, whatever it is? What things do they long to look into?
Being Holy as God is Holy
First Peter 1:13-18 “Therefore, preparing your minds for action, and being sober-minded, set your hope fully on the grace that will be brought to you at the revelation of Jesus Christ. As obedient children, do not be conformed to the passions of your former ignorance, but as he who called you is holy, you also be holy in all your conduct, since it is written, “You shall be holy, for I am holy.” And if you call on him as Father who judges impartially according to each one’s deeds, conduct yourselves with fear throughout the time of your exile, knowing that you were ransomed from the futile ways inherited from your forefathers, not with perishable things such as silver or gold.”
How can we possibly be holy when we all fall short of the glory of God (Rom 3:23)? What does it mean to conduct ourselves with fear? Why does Peter say we’re to conduct ourselves “with fear throughout the time of [our] exile?” What exile is he writing about? What action are we to prepare our minds for?
The Foreknown Lamb of God
First Peter 1:19-21 “but with the precious blood of Christ, like that of a lamb without blemish or spot. He was foreknown before the foundation of the world but was made manifest in the last times for the sake of you who through him are believers in God, who raised him from the dead and gave him glory, so that your faith and hope are in God.”
In what way was the Lamb of God foreknown before the foundation of the world? How can this be foreknown even before there was a man on the earth to sin? Did God know ahead of time that a spotless, blemish free lamb sacrifice would be necessary? Was it because of our nature? How has it been made manifest in these last times…and for our sake?
The Imperishable Seed
First Peter 1:22-25 “Having purified your souls by your obedience to the truth for a sincere brotherly love, love one another earnestly from a pure heart, since you have been born again, not of perishable seed but of imperishable, through the living and abiding word of God; for “All flesh is like grass and all its glory like the flower of grass. The grass withers, and the flower falls, but the Word of the Lord remains forever. And this word is the good news that was preached to you.”
I thought we were purified by Christ’s sacrifice (2 Cor 5:21) so how can our souls be purified by obedience? How can we love with a pure heart since “The heart is deceitful above all things, and desperately sick; who can understand it” (Jer 17:9)? What is this imperishable seed? Is it the Holy Spirit? Is this “good news that was preached to” us the gospel?
I hope you gain as much as I did in studying this first chapter of 1st Peter. There is so much there and in fact, every verse and chapter contain so much that you can spend years in one book giving messages and providing Bible studies. That’s how powerful and compact the Word of God is. There is depth in an economy of even a few verses. Maybe you can come up with your own questions or even better ones than I came up with for this Bible study. Either way, it is hoped that it will help you grow in the grace and knowledge of the King of kings and Lord of lords, Jesus Christ.
More reading: What Does the Bible Teach About Free Will and Predestination? 
Resource – Scripture quotations are from The Holy Bible, English Standard Version® (ESV®), copyright © 2001 by Crossway, a publishing ministry of Good News Publishers. Used by permission. All rights reserved.