I have read a couple different conflicting answers on what happens if something like an arcane trickster multiclasses with one level of wizard. As far as I understand it, the arcane trickster would be 1 level ahead on spell slots. One post I read said that they would have access to level to level 5 spell slots by level 17. Another said that they do not follow that table in chapter 6 and instead round casting levels up. I would appreciate it if someone could clear this up for me. Thanks
A level 13 Arcane Trickster has access to 1st, 2nd and 3rd level spells and slots. He just learned third level spells. To reach level four spells, he must take another six levels of Arcane Trickster (per the table on page 98 Tricksters get 4th level spells at level 19).
What happens if he instead begins levelling as Wizard?
The first level of Wizard (now we're a level 14 character; 13 trickster/1 wizard) makes me a multiclass spellcaster of level 13/3+1=5. This is just enough to let us keep our third level spell slots.
But if we continue levelling as Wizard, with our third level of Wizard we finally gain 4th level spell slots as a level 7 multiclass spellcaster. At this time we are a level 16 character (13 trickster/3 wizard).
We are a level 7 multiclass spellcaster because our 13 trickster levels count as 13/3=4 levels, and our 3 wizard levels count as 3 levels. 4+3=7.
We are still a 16th level character. We still have 13 levels of Rogue (Arcane Trickster) and 3 levels of Wizard.
We still know
spells like that 13th level Trickster and level 3 Wizard. This means we know first, second and third level spells
as a Trickster. We also get to choose first and second level spells
as a wizard.
But we have
fourth level spell slots. Even though we have no actual level 4 spells to cast.
We can still use our level 4 slots to cast the spells we know as higher-levelled spells. Many spells do more damage or have other bigger effects when cast using higher-levelled slots.
In the end, by multiclassing, we reached 4th level
slots sooner, but we did not get any level 4
spells to go with them. Our level 4 slots are still useful, only not as useful. We can still treat them as extra powerful third level slots.