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Question

Question: \[\frac{\mathbf{2.}\mathbf{3}^{\mathbf{n + 1}}\mathbf{+ 7.}\mathbf{3}^{\mathbf{n}\mathbf{-}\mathbf{1...

2.3n+1+7.3n−13n+2−2(1/3)l−n=\frac{\mathbf{2.}\mathbf{3}^{\mathbf{n + 1}}\mathbf{+ 7.}\mathbf{3}^{\mathbf{n}\mathbf{-}\mathbf{1}}}{\mathbf{3}^{\mathbf{n + 2}}\mathbf{-}\mathbf{2(1/3}\mathbf{)}^{\mathbf{l}\mathbf{-}\mathbf{n}}}\mathbf{=}

A

1

B

3

C

–1

D

0

Answer

1

Explanation

Solution

2.3n+1+7.3n−13n+2−2(13)1−n=2.3n−1.32+7.3n−13n−1.33−2.3n−1=3n−1[18+7]3n−1[27−2]=1\frac{2.3^{n + 1} + 7.3^{n - 1}}{3^{n + 2} - 2\left( \frac{1}{3} \right)^{1 - n}} = \frac{2.3^{n - 1}.3^{2} + 7.3^{n - 1}}{3^{n - 1}.3^{3} - 2.3^{n - 1}} = \frac{3^{n - 1}\lbrack 18 + 7\rbrack}{3^{n - 1}\lbrack 27 - 2\rbrack} = 1