JEE Main 2018
Matrices & Determinants
Matrices and Determinants
Medium
Question
If are in G.P., then the value of the determinant \left| {\matrix{ {\log {a_n}} & {\log {a_{n + 1}}} & {\log {a_{n + 2}}} \cr {\log {a_{n + 3}}} & {\log {a_{n + 4}}} & {\log {a_{n + 5}}} \cr {\log {a_{n + 6}}} & {\log {a_{n + 7}}} & {\log {a_{n + 8}}} \cr } } \right|, is
Options
Solution
Key Concepts
This problem combines the properties of Geometric Progressions (G.P.), logarithms, and determinants.
- Geometric Progression (G.P.): A sequence of numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio (). The -th term of a G.P. is given by , where is the first term.
- Logarithm Properties:
- **Arithmetic Progression (A.