djstein02p8piub djstein02p8piub

24-10-2018
Mathematics

contestada

What is the explicit rule for this geometric sequence?

2/9,2/3,2,6,...

an=3(2/9)^n−1

an=2/9⋅3^n−1

an=2/9⋅3^n

an=3(2/9)n

Respuesta :

24-10-2018

[tex]a_1=\dfrac{2}{9},\ a_2=\dfrac{2}{3},\ a_3=2,\ a_4=6,\ ...\\\\r=a_2:a_1\\\\r=\dfrac{2}{3}:\dfrac{2}{9}=\dfrac{2}{3}\cdot\dfrac{9}{2}=3\\\\a_n=a_1r^{n-1}\\\\\boxed{a_n=\dfrac{2}{9}\cdot3^{n-1}}[/tex]

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