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P.o.t.W. #11 Solution

Let \({u_1},\;{u_1}r and \({u_1}{r^2} be the three consecutive terms of the geometric sequence. If \({u_1} and \({u_1}r are the first and fourth terms, respectively, of an arithmetic sequence then \({u_1}r - {u_1} = 3d ; and if \({u_1}r and \({u_1}{r^2} are the first and eighth terms, respectively, then \({u_1}{r^2} - {u_1} = 7d . Solving for \(d in each of these equations gives:...

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