A visiting preacher referred to I Chronicles 2:13-15 to show that Eliab was the eldest. In that section, it shows that Jesse had seven sons and that David was the seventh. But I Samuel 17:13 says that Jesse had 8 sons. The reason it caught my attention is that I had just worked up lessons on this section a couple of quarters ago for the primary class that I teach. I remember distinctly having questions that referred to Jesse having eight sons and David being the eighth. I want to make sure I have the correct answer so that I don't teach it incorrectly and make the corrections to the materials I wrote if need be.
"Now David was the son of that Ephrathite of Bethlehem Judah, whose name was Jesse, and who had eight sons. And the man was old, advanced in years, in the days of Saul. The three oldest sons of Jesse had gone to follow Saul to the battle. The names of his three sons who went to the battle were Eliab the firstborn, next to him Abinadab, and the third Shammah. David was the youngest. And the three oldest followed Saul" (I Samuel 17:12-14).
"Jesse begot Eliab his firstborn, Abinadab the second, Shimea the third, Nethanel the fourth, Raddai the fifth, Ozem the sixth, and David the seventh" (I Chronicles 2:13-15).
The difference is due to the time frame in which these two accounts were written. Jesse had eight sons and two daughters (I Chronicles 2:16) at the time that I Samuel was written. The most natural conclusion is to suppose that one of Jesse's sons died at a young age. At the time I Chronicles was written, only seven sons were living. Because I Chronicles is the only list of names for Jesse's sons, we don't know the name of the son who died.
The Hebrews were no different than we are today. If a person dies young before he marries, has children, or does something significant in the world, he tends to be skipped. For instance, I have a brother with who lost a son at the age of two weeks. He and others often talk about his four sons even though he had five sons. Often talking about the four sons is easier because it doesn't lead to awkward questions and stir up the heartache of the lost son. A genealogist is interested in the detailed list, but in day-to-day life, we are more interested in who has an active part in life.