SSC CGL 6 Sep 2016 Paper

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Question : 63 of 100

Marks: +1, -0

The value of

{3×9^{n+1}+9×3^{2n-1}}/{9×3^{2n}-6×9^{n-1}}

is equal to

3 $3/5$
3 $2/5$
3 $1/5$
3

Solution:

Expression
=

{3×9^{n+1}+9×3^{2n-1}}/{9×3^{2n}-6×9^{n-1}}

=

{3×(3^2)^{n+1}+3^2×3^{2n-1}}/{3^2×3^{2n}-6×(3^2)^{n-1}}

=

{3^{2n+2+1}+3^{2n-1+2}}/{3^{2n+2}-6×3^{2n-2}}

=

{3^{2n+3}+3^{2n+1}}/{3^{2n+2}-6×3^{2n-2}}

=

{3^{2n+1}(3^2+1)}/{3^{2n-2}(3^4-6)}

=

3^{2n+1-2n+2} ({10}/{75})

=

{3^3×10}/{75}

=

{27×10}/{75}

=

{18}/5

= 3

3/5

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