INCONSEQUENTLY

inconsequently, inconsequentially

(adverb) lacking consequence; “‘You’re so beautifully dressed,’ she said and added quite inconsequentially, ‘Can you stay the night?’”

Source: WordNet® 3.1

Etymology

Adverb

inconsequently (comparative more inconsequently, superlative most inconsequently)

In an inconsequential way, or a way that suggests a lack of consequence

Source: Wiktionary

INCONSEQUENT

In*con"se*quent, a. Etym: [L. inconsequens: cf. F. inconséquent. See In- not, and Consequent.]

Definition: Not following from the premises; not regularly inferred; invalid; not characterized by logical method; illogical; arbitrary; inconsistent; of no consequence. Loose and inconsequent conjectures. Sir T. Browne.

Source: Webster’s Unabridged Dictionary 1913 Edition