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  • 12-12-2018
  • Mathematics
contestada

What is the recursive rule for this geometric sequence? 2, 1/2, 1/8,  1/32,  

Enter your answers in the blanks.

an= _ ⋅an−1

a1=_

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gmany
gmany gmany
  • 18-12-2018

[tex]a_1=2,\ a_2=\dfrac{1}{2},\ a_3=\dfrac{1}{8};\ a_4=\dfrac{1}{32}\\\\r=\dfrac{a_2}{a_1}=\dfrac{a_3}{a_2}=\dfrac{a_4}{a_3}=...\\\\r=\dfrac{\frac{1}{2}}{2}=\dfrac{\frac{1}{8}}{\frac{1}{2}}=\dfrac{\frac{1}{32}}{\frac{1}{8}}=\dfrac{1}{4}\\\\\boxed{a_1=2;\qquad a_n=\dfrac{1}{4}\cdot a_{n-1}}[/tex]

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