How can it be that Zecharyah become king in Azaryah's 38th year, after Yaravam died? If Azaryah became king after his father died in Yaravam's 15th year, and Yaravam ruled 41 years in all, he died in Azaryah's 27th year!
Rashi: This shows that Azaryah and Yaravam became king the same year, just Yaravam ruled three years in the lifetime of his father Yo'ash. This is why it says "Yashav Al Kis'o" (13:13) - he already sat 1 on it. Azaryah became king after Yo'ash died, and then Yaravam ruled absolutely. Seder Olam says that Yaravam ruled one year in his father's lifetime. Perhaps this is a printing mistake. The only way to resolve why it says here '38' is like I explained.
Radak: Perhaps Zecharyah became king in the lifetime of his father Yaravam, 11 years before Yaravam died. I do not know why, but it resolves the calculation.
We learn from the simple past tense, as opposed to va'Yeshev (future with the prefix Vov to switch it to past), like Rashi wrote in Bereishis; refer to Bereishis 4:1:1:1. (PF)