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3 and 4 .Determinants and Matrices
normal
If ${2^{{a_1}}},{2^{{a_2}}},{2^{{a_3}}},{......2^{{a_n}}}$ are in $G.P.$ then $\left| {\begin{array}{*{20}{c}}
{{a_1}}&{{a_2}}&{{a_3}} \\
{{a_{n + 1}}}&{{a_{n + 2}}}&{{a_{n + 3}}} \\
{{a_{2n + 1}}}&{{a_{2n + 2}}}&{{a_{2n + 3}}}
\end{array}} \right|$ is equal to
A
$2$
B
$2^3$
C
$0$
D
None
Solution
$a_{1}, a_{2}, a_{3}$ are in $A . P$
so $\quad {{\rm{R}}_2} \to {{\rm{R}}_2} – \left( {\frac{{{{\rm{R}}_1} + {{\rm{R}}_3}}}{2}} \right)$
$ \Rightarrow \boxed{\Delta = 0}$
Standard 12
Mathematics