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A particle moves in a straight line with...

A particle moves in a straight line with uniform acceleration and its distances from an origin O on the line (not necessarily the position at time t = 0) at times `t_(1), t_(2),t_(3)` are `d_(1), d_(2),d_(3)` respectively. Prove that if `t_(1), t_(2), t_(3)` form an A.P. whose common difference isd and `d_(1),d_(2),d_(3)` are in G.P. then the acceleration is`(sqrt(d_(1))-sqrt(d_(3)))^(2)/(d^(2))`

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