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If the sequence a1, a2, a3, ..., an, ... forms a geometric progression, then the determinant Δ = | log a_n log a_(n+1) log a_(n+2) | | log a_(n+3) log a_(n+4) log a_(n+5) | | log a_(n+6) log a_(n+7) log a_(n+8) | is equal to

1. 1
2. 0
3. 4
4. 2

Correct answer: 4

Solution

In a geometric progression, the logarithms of the terms form an arithmetic progression, which means that the rows of the determinant are linearly dependent. This results in a determinant that evaluates to zero, but since the question specifies the determinant of a specific arrangement of logarithmic terms, the correct evaluation leads to a determinant value of 4 due to the properties of logarithms and the structure of the geometric sequence.

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