Lexical Definition

‎ἆρα‎ âra (ar'-ah) no? ^G:PRT-N
a form of ‎ἄρα‎, denoting an interrogation to which a negative answer is presumed

therefore.

Abbott-Smith

ἆρα, interrog. particle, implying anxiety or impatience, "quite rare and only in Luke and Paul, therefore a literary word" (Bl., §77, 2).
1. (num igitur) expecting a neg. reply, Lk 18:8; ἆρά γε, Ac 8:30.
2. (ergone) in apodosis, expecting an affirm. reply, Ga 2:17 (Bl., §77, 2; Lft., Ga., in l.; MM, s.v.).†

Abbott-Smith References

Liddell-Scott-Jones

ἆρα,

interrogative Particle, implying anxiety or impatience, = Epic dialect and Lyric poetry ἦ ῥα:

__1 alone, it simply marks the question, the nature of which is determined by the context: e.g. in [Refs 4th c.BC+] a negative answer is implied in the question ἆρ᾽ ἂν οἴεσθε..; but an affirmative in [Refs 5th c.BC+] ἆ. βέβληκα δὶς ἐφεξῆ; compare ἆρ᾽ εὐτυχεῖς.. ἢ δυστυχεῖ; [Refs 5th c.BC+]; and to make it plainly affirmative, ἆρ᾽ ο; ἆρ᾽ οὐχ; [Refs 5th c.BC+]; ἆρ᾽ οὐχ οὕτω; [Refs 5th c.BC+]
__2 ἆ. οὖ; is used to draw an affirmative inference, [Refs]; also when a negative answer is expected, [Refs]; with a negative, ἆρ᾽ οὖν οὐ..; [Refs]
__3 in ἆρά γε, each Particle retains its force, γε serving to make the question more definite, [Refs 5th c.BC+]
__4 less frequently with τίς interrogative, τίνος ποτ᾽ ἆρ᾽ ἔπραξε χειρί[Refs 5th c.BC+]; τίδ᾽ ἆρ᾽ ἐγὼ σ; [Refs 5th c.BC+]; with ἤν, [Refs 5th c.BC+]
__5 in indirect questions, σκεψώμεθα τοῦτο ἆ... [Refs 5th c.BC+]
__II in Poets sometimes like{ἄρα}, [Refs 7th c.BC+]
__B In Prose, ἆ. almost always stands first in the sentence, but[Refs 5th c.BC+]; καὶ ὑπὲρ τούτων ἆ... [Refs 4th c.AD+]