Sequences of chords, and the relationship of one chord to the next

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Ic-V-I perfect cadence progression SATB part writing rules

I am studying Music at AS-level - we have to harmonise a soprano line (in any style we wish I believe) with the alto, tenor and bass parts. One possible perfect cadence I have been taught is the ...
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Does the three chord trick always end a chord progression on the third chord?

It seems almost a redundant question, but the meat of it is this: If one is using the three chord trick, is it stylistically required by rules of theory and phrasing to end the progression on the ...