Cast off on jumper neck

Ive been knitting a jumper for a year project and am a bit stuck with how to finish off the back.

I have done as far as - Cast off 18sts, P52, I’m not sure how to continue

Welcome to KH!
Good progress so far. There’s one thing. Check the cast off. As I see it, you’re making the 3rd size and in that case you should cast off 15sts, then purl the next 52sts. That’ll leave you with 53sts on the right hand needle because there’ll also be the single stitch leftover from casting off. Now cast off the remaining 15sts and place the center 53sts on a holder.

So should i cast off the last 15sts in purl?

Yes, that’ll work.
One other possibility if you’d like is to leave the shoulder sts on the needle, slip them to a holder and later join them to the front or back with 3-needle bind off. It works very well and produces a sturdy seam. It’s up to you.