That´s because "gördüğüm" is not the verb. "Örümcektir" is the verb, shortened as "örümcek."

Bu gördüğüm ilk Türk örümcek(tir).

You made me write Türk örümcek damn you!! What is a Türk örümcek? A Turkish spider? What´s the story behind this? Did you see its passport? Or is it the name for a species of spider? Or do you mean "this is the first spider I´ve seen in Turkey"?

Please do not help me anymore.

OK I won´t help anymore. So what´s the deal with the Turkish spider?

http://www.turkishclass.com/turkish_lesson_331 Word order, syntax

Yes, the predicates locate at the end of a sentence in Turkish normally. One can change their locations as long as it is needed to emphasize.