The first, second and third terms of a geometric progression are the first, fifth and eighth terms

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The first, second and third terms of a geometric progression are the first, fifth and eighth terms respectively of an arithmetic progression. Given that the first term in each progression is 200 and the common ratio of the geometric progression is r, where r ≠ 1, find

a. The value of r

b. The fourth term of each progression

c. The sum to infinity of the geometric progression.

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