Flight Crew Air Transport Pilot (ATP)
Distraction; Situational Awareness
Deviation - Track / Heading All Types; Deviation / Discrepancy - Procedural Published Material / Policy; Inflight Event / Encounter CFTT / CFIT; Inflight Event / Encounter Unstabilized Approach
Flight Crew Executed Go Around / Missed Approach; Flight Crew Became Reoriented
Human Factors
We were level at 3;000 flying base vectors for the ILS RWY 5R at IND. We were given at turn to intercept and cleared for approach at or above 2;500 MSL. We started the turn; but I did not arm the approach. Just as it was apparent we were going to not intercept; the Pilot Monitoring mentioned I needed to arm the approach. I adjusted the heading to avoid overshoot; but we still ended up overshooting. The Approach Controller gave just a heading to again intercept. I had the LOC armed; but neglected to arm approach. This time; we did intercept; but since I had only pushed LOC; we were not descending and were high on the approach. When we realized this; I disengaged the autopilot and tried to increase descent with speed brake. Our configuration was gear down; flaps 20; with speed brake out. Our sink rate caused the GPWS to call out 'sink rate.' We decided to initiate a go-around; as we were not going to be stable. Tower asked us our reason and we told them we were not stable. The Controller said no problem and had us continue to 3;000 and handed us back to Approach. We were vectored back around and fly the same 5R approach and landed. As Pilot Flying; I did not arm the Approach when cleared. This started a chain of errors which included me then only arming LOC when again; I should have armed Approach. One factor that did distract us was the ATC radios as we arrived in the 25 NM area of IND. It was extremely busy and many were given vectors off the GIBBS arrival; only to be directed back to Knight.  There were a couple aircraft who received runway changes and another aircraft who answered instructions that were not meant for them. I really got engulfed trying to figure out how our aircraft was going to work in the sequence. I let this distract me too much from also focusing on flying the aircraft correctly (i.e.; get cleared and arm the Approach mode).Don't forget basic procedures like arming the approach when cleared and in a position to intercept localizer course.
As we recaptured the localizer and approaching the glideslope we were told to contact tower. During the frequency change I noticed we had not captured the glideslope and realized Pilot Flying had not armed it; only the localizer and stated such; and he armed it but we were already above the glideslope and I told him we have to descend to it. I think he then disconnected the autopilot to fly down to the glideslope and we heard the GPWS 'sink rate; sink rate'. As he arrested the sink rate we then heard 'terrain; terrain'. As I commanded a go-around we then broke out of the clouds and could see we were level flight and still had one white light on the PAPI so I told him 'OK; continue'. It proved too difficult to do as he had already depressed the Takeoff Go Around (TOGA) switch and the flight guidance was not appropriate; so I again commanded 'go around'. I then contacted tower for the first time and told them we were going around. I don't believe we ever got below 1;000 feet AGL. We were then vectored around for an uneventful second approach and landing.
Air carrier flight crew reported executing a go-around after the approach became unstabilized following failure to arm the approach mode.