If a, b, c are in G.P., show that `a^(2) + b^(2), ab + bc` and `b^(2) + c^(2)` are also in G.P.

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If \( a, b, c, d \) are in G.P., show that \[ (b-c)^{2}+(c-a)^{2}+(d-b)^{2}=(a-d)^{2} . \] If \( a, b, c, d \) are in G.P., show that \[ (b-c)^{2}+(c-a)^{2}+(d-b)^{2}=(a-d)^{2} . \]