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if  a_{1},a_{2},a_{3},......,a_{n},.... are G.P. then the value of the determinant

  is

  • Option 1)

    2

  • Option 2)

    1

  • Option 3)

    0

  • Option 4)

    -2

 

Answers (2)

As we learnt in 

Property of determinant -

If each element in a row ( or column ) of a determinant is written as the sum of two or more terms then the determinant can be written as the sum of two or more determinants

- wherein

 

 \begin{vmatrix} \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} \end{vmatrix}

 

\Rightarrow C_2\rightarrow C_2-C_1\ and\ C_3=C_3-C_2

\begin{vmatrix} \log a_{n} &\log\frac{a_{n+1}}{a_n} &\log\frac{a_{n+2}}{a_{n+1}} \\ \log a_{n+3}&\log\frac{a_{n+4}}{a_{n+3}} & \log\frac{a_{n+5}}{a_{n+4}} \\ \log a_{n+6} &\log\frac{a_{n+7}}{a_{n+6}} &\log\frac{a_{n+8}}{a_{n+7}} \end{vmatrix}

Now \frac{a_{n+2}}{a_{n}}= r

similarly \frac{a_{n+2}}{a_{n+1}}= r

and so on.

\begin{vmatrix} \log a_n &r &r \\ \log a_{n+3}&r &r \\ \log a_{n+6}& r &r \end{vmatrix}= 0

 


Option 1)

2

Incorrect option

Option 2)

1

Incorrect option

Option 3)

0

Correct option

Option 4)

-2

Incorrect option

Posted by

Vakul

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