A Geometric Progression Problem

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There is an initial investigation of geometric progressions where the interval between the first and second, and the third and fourth terms are given, with the challenge of discovering two possible values for the first term and associated common ratio. There are ten examples to work on to enable collaboration between groups.

A subsequent problem gives the information that the second term of a geometric progression is greater than the first term by 20, the challenge is to determine by what amount the fourth term should be greater than the first to yield a unique solution. Determining the result requires factorisation and then solution of a quadratic equation. 

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