#1038 · Algebra · Sequences & series

Relation among four consecutive G.P. terms

Let $a, b, c, d$ be four consecutive terms of a geometric progression. Prove that $(b - c)^{2} + (c - a)^{2} + (d - b)^{2} = (a - d)^{2}$ .

~7 minProof · checked by AIGeometric progressionAlgebraic identity

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. V. Geometrical Progression, Examples V.b, No. 17

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