The first, second and third terms of a geometric progression are the first, sixth and ninth terms,

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The first, second and third terms of a geometric progression are the first, sixth and ninth terms, respectively, of an arithmetic progression. Given that the first term in each progression is 100 and the common ratio of the geometric progression is r, where r ≠ 1, find: 

a. The value of r
b. The fifth term of each progression.

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