Respuesta :

The [tex]12^{th}[/tex] of the given sequence is 0.125, if the sequence is 256, 128, 64, 32, ... etc. Which is obtained by the formula of [tex]N_{n}= \frac{F}{ 2^(n-1) }[/tex].

Step-by-step explanation:

The given is,

                 The sequence 256, 128, 64, 32,...

Step:1

                Formula to calculate the [tex]n^{th}[/tex] therm of the given sequence,

                                                   [tex]N_{n}= \frac{F}{2^(n-1) }[/tex].............................(1)

                Where, F - First value

                             n - Term which is to calculate

               From given,

                           F = 256

                           n = 12

              Equation (1) becomes,

                                                [tex]N_{12}= \frac{256}{2^(12-1) }[/tex]

                                                [tex]N_{12}= \frac{256}{2^{11} }[/tex]

                                                       [tex]= \frac{256}{2048}[/tex]

                                                       [tex]=0.125[/tex]

                                                [tex]N_{12}[/tex] = 0.125

                                                         ( or )

Step:1

     The given sequence is based on,

     To find the next value in sequence the previous value is divided by 2

         The [tex]1^{st}[/tex] term is 256

         For the [tex]2^{nd}[/tex] term = [tex]\frac{Previous value}{2}[/tex] = [tex]= \frac{256}{2}[/tex] = 128

         For the [tex]3^{rd}[/tex] term [tex]= \frac{128}{2}[/tex] = 64

         For the [tex]4^{th}[/tex] term  [tex]= \frac{64}{2}=32[/tex]

         For the [tex]5^{th}[/tex] term  [tex]= \frac{32}{2}=16[/tex]

         For the [tex]6^{th}[/tex] term  [tex]= \frac{16}{2}=8[/tex]

         For the [tex]7^{th}[/tex] term  [tex]= \frac{8}{2}=4[/tex]

         For the [tex]8^{th}[/tex] term  [tex]= \frac{4 }{2}=2[/tex]

         For the [tex]9^{th}[/tex] term  [tex]= \frac{2}{2}=1[/tex]

         For the [tex]10^{th}[/tex] term  [tex]= \frac{1}{2}=0.5[/tex]

         For the [tex]11^{th}[/tex] term  [tex]= \frac{0.5}{2}=0.25[/tex]

         For the [tex]12^{th}[/tex] term  [tex]= \frac{0.25}{2}=0.125[/tex]

        The sequence becomes,

                      256, 128, 64,32,16, 8, 4, 2, 1, 0.5, 0.25, 0.125,..

Result:

           The [tex]12^{th}[/tex] of the given sequence is 0.125, if the sequence is 256, 128, 64, 32, ... etc. Which is obtained by the formula of [tex]N_{n}= \frac{F}{ 2^(n-1) }[/tex].                          

Lanuel

The  twelfth (12) term of the sequence 256, 128 , 64 , 32...... is 0.125.

Given the following data:

  • First (1st) term = 256
  • Second term = 128
  • Third term = 64
  • Fourth term = 32

To find the twelfth (12) term of the sequence:

Mathematically, the [tex]n^{th}[/tex] term of a sequence is calculated by using the following formula;

[tex]N_n = \frac{First\; term}{2^{n - 1}}[/tex]

Substituting the given parameters into the formula, we have;

[tex]N_{12} = \frac{256}{2^{12 - 1}}\\\\N_{12} = \frac{256}{2^{11}}\\\\N_{12} = \frac{256}{2048}\\\\N_{12} = 0.125[/tex]

Therefore, the  twelfth (12) term of the sequence is 0.125.

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