The multiclassing rules on page 164-165 of the Player's Handbook make it clear that all characters approximately use the same spell slot progression table, which is that of the wizard and cleric, but some "secondary" caster classes progress at one half or one third of that rate:

Spell slots. You determine your available spell slots by adding together all your levels in the bard, cleric, druid, sorcerer, and wizard classes, half your levels (rounded down) in the paladin and ranger classes, and a third of your fighter or rogue levels (rounded down) if you have the Eldritch Knight or the Arcane Trickster feature.

You'll notice that this largely holds true for the paladin spell slot progression. They have no spells at all for the first level, because that would round down to zero, and their spell slots only change every two levels. It isn't exact, since the paladin gains his new slots at odd levels (5, 9, 13, 17), to match the other major casting classes. The ranger gains their spells at the same levels.

Primary spellcasting classes (bard, cleric, druid, sorcerer and wizard), as in those for whom spellcasting is their main ability, progress at the full rate. In other words, if you were to make a variant sorcerer, it should really use the standard sorcerer spell slot progression unless the class has other combat abilities like the paladin or eldritch knight fighter archetype does.

The multiclassing rules on page 164-165 of the Player's Handbook make it clear that all characters approximately use the same spell slot progression table, which is that of the wizard and cleric, but some "secondary" caster classes progress at one half or one third of that rate:

Spell slots. You determine your available spell slots by adding together all your levels in the bard, cleric, druid, sorcerer, and wizard classes, half your levels (rounded down) in the paladin and ranger classes, and a third of your fighter or rogue levels (rounded down) if you have the Eldritch Knight or the Arcane Trickster feature.

You'll notice that this largely holds true for the paladin spell slot progression. They have no spells at all for the first level, because that would round down to zero, and their spell slots only change every two levels. It isn't exact, since the paladin gains his new slots at odd levels (5, 9, 13, 17), to match the other major casting classes. The ranger gains their spells at the same levels.

Primary spellcasting classes (bard, cleric, druid, sorcerer and wizard), as in those for whom spellcasting is their main ability, progress at the full rate. In other words, if you want to make a variant sorcerer, it should really use the standard sorcerer spell slot progression unless the class has other combat abilities like the paladin or eldritch knight fighter archetype does.

The secondary caster table is for paladin and ranger, who are in a sense hybrids of fighter-cleric and fighter-druid, respectively. Spells are their secondary abilities, so they have half progression. It's not precisely half, as it seems that the designers tweaked the table so, for example, you gain your new slots and odd levels and gain a third spell per day at level 3 to beef you up early on, and so you gain something when the primary casters do.

The tertiary casters are those who are magic-using archetypes of a class that isn't normally a magic-using class. This is for the fighter or rogue who dabbles in magic, and isn't recommended for a variant sorcerer.

The multiclassing rules on page 164-165 of the Player's Handbook make it clear that all characters actually use the same spell slot progression table, which is that of the wizard and cleric, but some "secondary" caster classes progress at one half or one third of that rate:

Spell slots. You determine your available spell slots by adding together all your levels in the bard, cleric, druid, sorcerer, and wizard classes, half your levels (rounded down) in the paladin and ranger classes, and a third of your fighter or rogue levels (rounded down) if you have the Eldritch Knight or the Arcane Trickster feature.

The multiclassing rules on page 164-165 of the Player's Handbook make it clear that all characters approximately use the same spell slot progression table, which is that of the wizard and cleric, but some "secondary" caster classes progress at one half or one third of that rate:

Spell slots. You determine your available spell slots by adding together all your levels in the bard, cleric, druid, sorcerer, and wizard classes, half your levels (rounded down) in the paladin and ranger classes, and a third of your fighter or rogue levels (rounded down) if you have the Eldritch Knight or the Arcane Trickster feature.

You'll notice that this largely holds true for the paladin spell slot progression. They have no spells at all for the first level, because that would round down to zero, and their spell slots only change every two levels. It isn't exact, since the paladin gains his new slots at odd levels (5, 9, 13, 17), to match the other major casting classes. The ranger gains their spells at the same levels.

Primary spellcasting classes (bard, cleric, druid, sorcerer and wizard), as in those for whom spellcasting is their main ability, progress at the full rate. In other words, if you were to make a variant sorcerer, it should really use the standard sorcerer spell slot progression unless the class has other combat abilities like the paladin or eldritch knight fighter archetype does.