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It a(1) , a(2) , a(3) a(4) be in G.P. t...

It ` a_(1) , a_(2) , a_(3) a_(4)` be in G.P. then prove that `(a_(2)-a_(3))^(2) + (a_(3) - a_(1))^(2) + (a_(4) -a_(2))^(2) = (a_(1)-a_(4))^(2)`

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To prove that \((a_2 - a_3)^2 + (a_3 - a_1)^2 + (a_4 - a_2)^2 = (a_1 - a_4)^2\) given that \(a_1, a_2, a_3, a_4\) are in a geometric progression (G.P.), we can follow these steps: ### Step 1: Express the terms in G.P. Let \(a_1 = a\) and the common ratio be \(r\). Then we can express the terms as: - \(a_2 = ar\) - \(a_3 = ar^2\) - \(a_4 = ar^3\) ...
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