Final answer:
The appropriate word to fill the blank in the sentence is 'declined', indicating the action of refusing an invitation.
Step-by-step explanation:
The correct word to complete the sentence "I couldn't imagine being part of the club, so I **declined** the invitation to join." is indeed "declined." In this context, "declined" is the appropriate term to express the act of politely refusing or rejecting an invitation. When someone declines an invitation, it signifies their decision not to accept or participate in the proposed event or join a particular group, as suggested in the sentence.
This choice reflects a personal decision to abstain from involvement, conveying a sense of polite refusal. The word "declined" aptly captures the notion of respectfully turning down the invitation, emphasizing the individual's choice to not become a part of the mentioned club or activity.