Usage: 2 forms in 3 verses
Form Translated As     In Verse(s)
προθυμούμενοσ feeling eager LXX.2Chr.17.16
feeling eager to LXX.1Chr.29.5
προεθυμήθησαν were eager LXX.1Chr.29.6

Liddell-Scott-Jones

προθυμέομαι (prothumeomai) to feel eager G:V

προθυμέομαι-έομαι,

imperfect προὐθυμούμην [Refs 5th c.BC+] προεθ- (with variant{προθ-}), [Refs 5th c.BC+]: future προθυμήσομαι [Refs 5th c.BC+]; προθυμηθήσομαι variant in [Refs 5th c.BC+]: aorist προὐθυμήθην [Refs 5th c.BC+]: perfect προτεθύμημαι [Refs]:—to be ready, willing, eager to do a thing, with infinitive, [Refs 5th c.BC+]; ὃς ἂν προθυμεῖσθαι ἐθέλῃ δίκαιος γενέσθαι will show zeal in becoming.., [Refs 5th c.BC+]

__2 absolutely (though an infinitive may commonly be supplied), show zeal, exert oneself, [Refs 5th c.BC+]; to be of good cheer, in good spirits, opposed to ἀθυμέω, [Refs]
__3 with accusative objecti, to be eager or zealous for, desire ardently, τὴν ξύμβασιν, τὴν ὁμολογίαν, [Refs 5th c.BC+]: mostly with neuter adjective, π. τοῦτο, ὅπως.. [Refs 5th c.BC+]