If {2^{{a₁}}},{2^{{a₂}}},{2^{{a₃}}},{......2^{{aₙ}}} are in G.P. then $left| {begin{array}{*

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3 and 4 .Determinants and Matrices

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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

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