What do you say as an “invitation” at the end of a sermon?

Answer:

An "invitation" at the close of a sermon is a tradition and not a requirement. Not that it is a bad tradition, but we must understand that a person can obey the gospel call at any time, not just at the end of a sermon (see Offering an Invitation). In fact, the terminology is a bit off. We encourage people to obey the Lord, but the invitation to come is from the Lord and not from us.

Too many think that the gospel message is only about becoming a Christian. It is certainly a part of the message, but all the Bible is the good news from God. Talking about the Israelites who perished, the writer of Hebrews said, "For indeed we have had good news preached to us, just as they also; but the word they heard did not profit them, because it was not united by faith in those who heard" (Hebrews 4:2). We tend to forget that the gospel message has been being revealed since the fall of man. "And how shall they preach unless they are sent? As it is written: 'How beautiful are the feet of those who preach the gospel of peace, who bring glad tidings of good things!' But they have not all obeyed the gospel. For Isaiah says, 'Lord, who has believed our report?' So then faith comes by hearing, and hearing by the word of God. But I say, have they not heard? Yes indeed: 'Their sound has gone out to all the earth, and their words to the ends of the world'" (Romans 10:15-18).

When a preacher teaches lessons from the Bible, he is teaching the gospel. See: What Is the Gospel About? Obedience is not limited to becoming a Christian. For example, avoiding sin is a part of the gospel. "But we know that the Law is good, if one uses it lawfully, realizing the fact that law is not made for a righteous person, but for those who are lawless and rebellious, for the ungodly and sinners, for the unholy and profane, for those who kill their fathers or mothers, for murderers and immoral men and homosexuals and kidnappers and liars and perjurers, and whatever else is contrary to sound teaching, according to the glorious gospel of the blessed God, with which I have been entrusted" (I Timothy 1:8-11).

Thus, the best ending for sermons is one that encourages the audience to apply the message immediately to their lives. Remind those who may still be thinking about becoming a Christian that there is no better time than the present, or offer those who realize that their lives have not been right before God an opportunity to have their brethren pray to the Lord on their behalf. Make it clear that this isn't the only time it can be done, but there is an opportunity now, so why delay?

I do thank you for this particular question because as I put this answer together, I see that I should make some points clearer at the end of my lessons.