Using Romans 8:29
The term prooizo and proginosko are the terms used translated foreknow (proginosko) and foreknow/predestinate (prooizo).
Prooizo is a compound of pro, before, with the verb horizo, to ordain, determine, and means to preordain. This term is not used in the LXX.
"The NT uses prooizo 6x to speak exclusively of God's decrees. 1. Paul uses the vb. in Rom. 8:29 together with proginosko, foreknow (-->4589) and prothesis, plan, decision (-->4729), in order to ground God's call in his prior decree. In 8:30 proorizo is taken up again in order to specify the end to which God's dealings with humans are directed, namely, to justify those who are called and to give them a share in his glory. In 1 Cor 2:7 Paul speaks of God's wisdom that he himself "destined for our glory." God's predestination is thus described as an activity of his directed towards the fellowship of humans with him." p. 492
"In Paul proginosko demonstrates the character of God's activity among humans. It assumes a personal relationship wiht a group of people that originiates in God himself. Rom 8:29 declares that those whom "God foreknew he also predestined to be conformed to the like-ness of his Son." In 11:2 the vb. expresses God's election and love of Israel, which oppses the idea of a final rejection of Israel." p. 490-491
Source: New International Dictionary of New Testament Theology. Abridged Edition. Verlyn D. Verbruggee, Editor.
I give this just in interest of giving information. I think Spiros Zhodiates' Word Study is also worth sharing:
"In Rom 8:29, in relation to believers, proginosko occurs with the verb proorise, aor. act. indic. of proorizo (4309), to predestinate. Foreknowledge and foreordination are logically coordinate. The former emphasizes the exercise of God's wisdom and intelligence in regard to His eternal purpose and the latter emphasizes the exercise of God's will in regard to it. What He has decreed is what He has decided. This foreknowledge and foreordination in the Scripture are always unto salvation and not unto perdition. Therefore, it should be said that the Lord never foreordains something to be lost.
Rather, He foreordains unto salvation those whom He specially considered and chose in eternity past (see Matt. 7:23; John 10:14; Rom 11:2; 1 Cor 8:3; Gal 4:9; 2 Tim 2:19; Sept.: Hos. 13:5; Amos 3:2). Any thought of the lost being appointed or ordained unto condemnation should be understood as an act of passing over in which the lost are permitted to suffer the consequences of their choice of sin (1 Peter 2:8).
The salvation of every believer is known and determined in the mind of God before its realization in time. Thus, proginosko corresponds with the idea of having been chosen (eklegomai [1586], to choose) before the foundation of the world mention in Eph. 1:4 and logically precedes the action indicated by proorizo. Proginosko essentially entails a gracious self-determining on God's part from eternity to extend fellowship with Himself to undeserving sinners (Rom 8:29).
-p.1216 "The Complete Word Study"