Question

Encontre os cinco primeiros termos da P.G,tal que a1=1/3^28 e a10=1/3^10

Answer 1

$a_{10}=\dfrac{1}{3^{10}}\\\\\\a_{1}\cdot q^{9}=\dfrac{1}{3^{10}}\\\\\\\dfrac{1}{3^{28}}\cdot q^{9}=\dfrac{1}{3^{10}}\\\\\\q^{9}=\dfrac{3^{28}}{3^{10}}\\\\\\q^{9}=3^{18}\\\\\\q=3^{18/9}\\\\\\\boxed{\boxed{q=3^{2}}}$
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Cinco primeiros termos da P.G:

$a_{1}=\dfrac{1}{3^{28}}\\\\\\a_{2}=a_{1}\cdot q=\dfrac{1}{3^{28}}\cdot3^{2}=\dfrac{1}{3^{26}}\\\\\\a_{3}=a_{2}\cdot q=\dfrac{1}{3^{26}}\cdot3^{2}=\dfrac{1}{3^{24}}\\\\\\a_{4}=a_{3}\cdot q=\dfrac{1}{3^{24}}\cdot3^{2}=\dfrac{1}{3^{22}}\\\\\\a_{5}=a_{4}\cdot q=\dfrac{1}{3^{22}}\cdot3^{2}=\dfrac{1}{3^{20}}$