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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., then prove that a, c, e are in G.P.

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To prove that \( a, c, e \) are in geometric progression (G.P.), we will use the given conditions step by step. ### Step 1: Use the definition of A.P. for \( a, b, c \) Since \( a, b, c \) are in A.P., we have: \[ 2b = a + c \tag{1} \] ...
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