Question

O segundo termo uma pg é decrescente é 9/8 e o quarto é 1/2. Calcule o oitavo termo

Answer 1

$a_2=\dfrac{9}{8};\qquad{a}_4=\dfrac{1}{2};\qquad{a}_8=\ ?\\\\\\a_4=a_2\cdot{q}^2\longrightarrow\dfrac{1}{2}=\dfrac{9}{8}\cdot{q}^2\longrightarrow\dfrac{8}{18}=q^2\longrightarrow\dfrac{4}{9}=q^2\longrightarrow\sqrt{\dfrac{4}{9}}=q\longrightarrow\\\\{q}=\dfrac{2}{3}\\\\\\\\a_8=a_4\cdot{q}^4\longrightarrow{a}_8=\dfrac{1}{2}\cdot\left(\dfrac{2}{3}\right)^4\longrightarrow{a}_8=\dfrac{1}{2}\cdot\dfrac{16}{81}\longrightarrow\boxed{{a}_8=\dfrac{8}{81}}$