The "I - IV - V" or "i - iv - v" chord progression...

It is almost automatic the feeling when we hear a progression of a "one" chord going to a "four" chord and then finishing with a "fifth" chord on any key.

Something curious to note is that the same intervals could be found on the relative minor variations of the typical major I - IV - V chord progression...

Taking the key of "A major" for example, we find that the I is A major, the IV is D major, and the V is E major...all major because of their triad formulas. Right?  Still with me?  Post questions if you come up with any :)

Now, if we look at the same key of A major, and we set the 6th degree of that scale as its "relative" minor key (by the way, this is a fact in every major key...the 6th degree of any major key will always give you its relative minor!!!), we find that going from that 6th degree which can now become a "i" chord, the pattern of the minor "i - iv - v" is repeatable here too.  See the example on the paragraph below...

Example applied and explained:
F#m (that 6th degree in A major) - Bm (the 2nd degree in A major) - and C#m (the 3rd degree in A major)...also make a  "i - iv - v" progression.

So, in the same key of A major, we can find 2 sets of "one-four-five" sounding patterns of chord progressions.   The major I - IV - V or relative minor i - iv - v chord sequence.  The first sequence discussed speaks to the major key and the second sequence speaks to the relative minor key within that major key.

Again, this is a constant in every major and of course, relative minor key :)