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If a, b, c are in A.P., b, c, d are in G...

If a, b, c are in A.P., b, c, d are in G.P. and `1/c ,1/d ,1/e`are in A.P. prove that a, c, e are in G.P.

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To prove that \( a, c, e \) are in G.P. given the conditions that \( a, b, c \) are in A.P., \( b, c, d \) are in G.P., and \( \frac{1}{c}, \frac{1}{d}, \frac{1}{e} \) are in A.P., we can follow these steps: ### Step 1: Use the property of A.P. for \( a, b, c \) Since \( a, b, c \) are in A.P., we have: \[ 2b = a + c \quad \text{(1)} \] ...
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