If k − 1, k + 1 and k + 5 are in G.P. then the value of k is ______.

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If k − 1, k + 1 and k + 5 are in G.P. then the value of k is 3. Explanation: a = k − 1 b = k + 1 c = k + 5 (k + 1)2 = (k − 1)(k + 5) k2 + 2k + 1 = k2 + 5k − k − 5 k2 + 2k + 1 = k2 + 4k − 5 2k + 1 = 4k − 5 1 + 5 = 4k − 2k 6 = 2k k = $\frac{6}{3}$ k = 3

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