Respuesta :

devishri1977

Answer:

Step-by-step explanation:

First term = a = 1

common ratio = r = second term ÷ first term = 4 ÷ 1 = 4

nth term = [tex]ar^{n-1}[/tex]

11th terms = [tex]1*4^{10} = 4^{10}[/tex]

We've been given to find out the 11th term of a geometric sequence 1,4,16,64...

Here we have,

  • First term (a) = 1

  • Common ratio (r) = 4/1 = 4

  • n = 11

The standard formula for calculating the geometric sequence is given by,

[tex]:\implies\rm{ {n}^{th} \: term = {ar}^{n - 1} }[/tex]

Substituting values we get,

[tex]:\implies\rm{ {11}^{th} = 1 \times {4}^{11 - 1} }[/tex]

[tex]:\implies\rm{ {11}^{th} = {4}^{11 - 1} }[/tex]

[tex]:\implies\rm{ {11}^{th} = {4}^{10} }[/tex]

[tex]:\implies\rm{ {11}^{th} \: term = 1048576}[/tex]

  • The 11th term of G.P. is 4¹⁰.

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