From the multiclassing spellcasting rules (link is the PHB because Basic Rules version doesn't include Arcane Trickster): Rangers are half rounded down so 5 becomes 2 and Arcane Trickster is one third rounded down so 5 becomes 1 - for a total of 3. When you check the table you should have 4x 1st and 2x 2nd. And you are right - that is exactly the same as a 5th level Ranger would have.
Multiclassing causes things to work differently for the number of spell slots you get. For calculating what slots you should have, you add 1 for every level of full caster, 1/2 for every level of half-caster (Ranger) rounded down, and 1/3 for every level of 3rd-caster (Arcane Trickster) rounded down. This means that you get the slots of a 5/2 + 5/3 = 2 + 1 = level 3 full caster, who has 4 lv1 and 2 lv2 slots, so yeah, it would look like the same slots as for a 5th-level single-classed Ranger..
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How many spell slots should this character have?
I think it should have the sum of both classes, am I right?
It apparently has only the slots of the ranger
From the multiclassing spellcasting rules (link is the PHB because Basic Rules version doesn't include Arcane Trickster): Rangers are half rounded down so 5 becomes 2 and Arcane Trickster is one third rounded down so 5 becomes 1 - for a total of 3. When you check the table you should have 4x 1st and 2x 2nd. And you are right - that is exactly the same as a 5th level Ranger would have.
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Multiclassing causes things to work differently for the number of spell slots you get. For calculating what slots you should have, you add 1 for every level of full caster, 1/2 for every level of half-caster (Ranger) rounded down, and 1/3 for every level of 3rd-caster (Arcane Trickster) rounded down. This means that you get the slots of a 5/2 + 5/3 = 2 + 1 = level 3 full caster, who has 4 lv1 and 2 lv2 slots, so yeah, it would look like the same slots as for a 5th-level single-classed Ranger..
Helpful rewriter of Japanese->English translation and delver into software codebases (she/e/they)
But add 1 more level of each to get a big ol' jump to lv3 slots! You just won't get to learn level 3 spells though.
Helpful rewriter of Japanese->English translation and delver into software codebases (she/e/they)