maxwellbob2301 maxwellbob2301
  • 25-07-2018
  • Mathematics
contestada

in a geometric sequence, a^11=72 and a^13=1/2. use the geometric mean to find the value of a^12

Respuesta :

gmany
gmany gmany
  • 26-07-2018

If a, b, c is a geometric sequence, then [tex]ac=b^2[/tex]

We have:

[tex]a_{11}=72;\ a_{12};\ a_{13}=\dfrac{1}{2}[/tex]

substitute:

[tex](a_{12})^2=72\cdot\dfrac{1}{2}\\\\(a_{12})^2=36\to a_{12}=\pm\sqrt{36}\\\\a_{12}=-6\ \vee\ a_{12}=6[/tex]

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