Step 1: The parathyroid glands develop from the dorsal parts of the pharyngeal (branchial) pouches, not the arches themselves, but the pouch lies between arches and the inferior parathyroid is conventionally linked to the third pouch and its arch.
Step 2: The inferior parathyroid arises from the dorsal wing of the 3rd pharyngeal pouch. The same 3rd pouch also gives rise to the thymus, which is why these two structures share a developmental origin.
Step 3: Because the thymus migrates caudally and drags the inferior parathyroid down with it, the inferior parathyroid ends up below the superior parathyroid - which itself comes from the 4th pouch.
Step 4: Therefore the inferior parathyroid develops in association with the 3rd arch / pouch, and the answer is 3rd.