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If A =open square brackets table row 3 cell negative 4 end cell row 1 cell negative 1 end cell end table close square brackets, then for every positive integer n, An is equal to -

  1. open square brackets table row cell 1 plus 2 n end cell cell 4 n end cell row n cell 1 plus 2 n end cell end table close square brackets    
  2. open square brackets table row cell 1 plus 2 n end cell cell negative 4 n end cell row n cell 1 minus 2 n end cell end table close square brackets    
  3. open square brackets table row cell 1 minus 2 n end cell cell 4 n end cell row n cell 1 plus 2 n end cell end table close square brackets    
  4. None of these    

The correct answer is: open square brackets table row cell 1 plus 2 n end cell cell negative 4 n end cell row n cell 1 minus 2 n end cell end table close square brackets


    we are given A and need to find A to the power of n
    A equals open square brackets table row 3 cell negative 4 end cell row 1 cell negative 1 end cell end table close square brackets
therefore A squared equals open square brackets table row 3 cell negative 4 end cell row 1 cell negative 1 end cell end table close square brackets open square brackets table row 3 cell negative 4 end cell row 1 cell negative 1 end cell end table close square brackets
space equals open square brackets table row 5 8 row 2 5 end table close square brackets
therefore A cubed equals open square brackets table row 5 8 row 2 5 end table close square brackets open square brackets table row 3 cell negative 4 end cell row 1 cell negative 1 end cell end table close square brackets space
therefore A cubed space equals open square brackets table row 7 12 row 3 7 end table close square brackets
therefore A to the power of 4 equals open square brackets table row 7 12 row 3 7 end table close square brackets open square brackets table row 3 cell negative 4 end cell row 1 cell negative 1 end cell end table close square brackets
therefore A to the power of 4 space equals open square brackets table row 9 16 row 4 9 end table close square brackets
therefore A to the power of n space space equals open square brackets table row cell 1 plus 2 n end cell cell 4 n end cell row cell space n end cell cell space space space ​ space space space space space 1 plus 2 n space ​ space end cell end table close square brackets

    Therefore the correct option is choice 2

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