Was David the 7th or 8th son of Jesses? I ask because of the two following scriptures:
1 Samuel 16:7-11 NIV  But the Lord said to Samuel, “Do not consider his appearance or his height, for I have rejected him. The Lord does not look at the things man looks at. Man looks at the outward appearance, but the Lord looks at the heart.”  Then Jesse called Abinadab and had him pass in front of Samuel. But Samuel said, “The Lord has not chosen this one either.”  Jesse then had Shammah pass by, but Samuel said, “Nor has the Lord chosen this one.”  Jesse had seven of his sons pass before Samuel, but Samuel said to him, “The Lord has not chosen these.”  So he asked Jesse, “Are these all the sons you have?” “There is still the youngest,” Jesse answered, “but he is tending the sheep.” Samuel said, “Send for him; we will not sit down until he arrives.”
1 Chronicles 2:13-15 NIV  Jesse was the father of Eliab his firstborn; the second son was Abinadab, the third Shimea,  the fourth Nethanel, the fifth Raddai,  the sixth Ozem and the seventh David. Reading the first passage in 1 Samuel, it leads the reader to believe that all 7 sons of Jesse’s had passed before Samuel and David tending the sheep should have been the youngest last 8th son to pass before Samuel to get anointed.
The explanation of the two passages is that 1 Sam 16:7-11 was written about a situation earlier in the life of David. 1 Chron 2:13-15 is a genealogy written much later. Apparently, one of the eight sons of Jesse died without having any children, so the only children of Jesse reported in the genealogy are those who were still alive or who still had descendants to keep track of. We know from other examples in biblical genealogies that when a child died “without issue” then they were generally not included in the genealogies. If you were to ask my wife how many kids were in her family, she would say there were ten. Actually, there were eleven, but one of them died as a fairly young child, so she and her siblings all say there were ten kids in the family. Probably this explains the apparent problem in the two passages.
It is possible that a copying error explains the difference, but I think this is less likely than a death in the family.
The lesson to be learned here is that when we see what may, at first glance, appear to be a “contradiction,” we should give the Bible the benefit of the doubt. The evidence for inspiration and inerrancy is sufficiently strong that when we see what can be thought of as a possible contradiction, we should assume, until further investigation, that the apparent contradiction is only apparent and not real.
I would use the analogy of my relationship with my wife. In the last 29 1/2 years she has earned the right to expect me to trust her (and vice versa). If I was presented with some evidence which could be construed that she was unfaithful to me, it would by unwise, foolish, unloving and even stupid for me to jump to the conclusion that she was probably cheating on me. The wise and reasonable approach, given the way she has acted the last thirty years is to assume that when I have all the information, I will conclude that it was completely innocent.
The Bible deserves even more of a “benefit of the doubt” than my wife. I suggest you approach future potential “contradictions” in the Bible in the same way. Do not ignore such information, as to ignore it is something which can come back to bite you in the future. Investigate the question, but in the initial phase, you should assume that almost certainly, there will turn out to be no real contradiction.