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**itsgotabigbirdonitdude** Different numbers x, y and z are the first three terms of a geometric progression with common ratio r, and also the first, second and fifth terms of an arithmetic progression.

a. Find the value of r.

b. Find which term of the arithmetic progression will next be equal to a term of the geometric progression.

I haven't tackled part b. yet but I'm guessing it must be quite straightforward once r is found, but for now I'm having major issues with a.

So far I've come up with r=y/x=z/y (since all are different versions of the common ratio of the geometric progression), z-y = 3(y-x) (since y-x is the common difference of the arithmetic progression and z-y is the difference between the second and fifth terms) and y-x = y/x.

However, I'm confused as to how to combine these equations in order to find r. All of my attempts have turned up hopelessly complex or just plain incorrect. Any suggestions as to the correct and most simple way to go about this would be appreciated, cheers.