A) Determine a razão de uma P.G em que A1= -3 e A4= -768.
B) Calcule a razão de uma P.G na qual o primeiro termo é 1/2 e o quarto termo é 4/21.
C) Calcule a razão de uma P.G na qual o primeiro termo é 1/4 e o quarto termo é 8/42.
Soluções para a tarefa
Respondido por
2
a) Usando a fórmula da PG, temos:
![\boxed{a_n=a_1*q^n^-^1}\\\\ a_4 = a_1*q^3\\\\ -768 = -3*q^3\\\\ q^3=\frac{-768}{-3}\\\\ q^3= 256\\\\ \boxed{q=4 \sqrt[3]{4}}](https://tex.z-dn.net/?f=%5Cboxed%7Ba_n%3Da_1%2Aq%5En%5E-%5E1%7D%5C%5C%5C%5C+a_4+%3D+a_1%2Aq%5E3%5C%5C%5C%5C+-768+%3D+-3%2Aq%5E3%5C%5C%5C%5C+q%5E3%3D%5Cfrac%7B-768%7D%7B-3%7D%5C%5C%5C%5C+q%5E3%3D+256%5C%5C%5C%5C+%5Cboxed%7Bq%3D4+%5Csqrt%5B3%5D%7B4%7D%7D "\boxed{a_n=a_1*q^n^-^1}\\\\ a_4 = a_1*q^3\\\\ -768 = -3*q^3\\\\ q^3=\frac{-768}{-3}\\\\ q^3= 256\\\\ \boxed{q=4 \sqrt[3]{4}}")
B)![a_4 = a_1*q^3\\\\ \frac{4}{21} = \frac{1}{2}*q^3\\\\ q^3=\frac{\frac{4}{21}}{\frac{1}{2}}\\\\ q^3 = \frac{8}{21}\\\\ \boxed{q = \frac{2}{\sqrt[3]{21}} }](https://tex.z-dn.net/?f=a_4+%3D+a_1%2Aq%5E3%5C%5C%5C%5C+%5Cfrac%7B4%7D%7B21%7D+%3D+%5Cfrac%7B1%7D%7B2%7D%2Aq%5E3%5C%5C%5C%5C+q%5E3%3D%5Cfrac%7B%5Cfrac%7B4%7D%7B21%7D%7D%7B%5Cfrac%7B1%7D%7B2%7D%7D%5C%5C%5C%5C+q%5E3+%3D+%5Cfrac%7B8%7D%7B21%7D%5C%5C%5C%5C+%5Cboxed%7Bq+%3D+%5Cfrac%7B2%7D%7B%5Csqrt%5B3%5D%7B21%7D%7D+%7D+ "a_4 = a_1*q^3\\\\ \frac{4}{21} = \frac{1}{2}*q^3\\\\ q^3=\frac{\frac{4}{21}}{\frac{1}{2}}\\\\ q^3 = \frac{8}{21}\\\\ \boxed{q = \frac{2}{\sqrt[3]{21}} }")
C)![a_4=a_1*q^3\\\\ \frac{8}{42} = \frac{1}{4}*q^3\\\\ q^3=\frac{\frac{8}{42}}{\frac{1}{4}}\\\\ q^3=\frac{32}{42}\\\\ q^3=\frac{16}{21}\\\\ \boxed{q=\frac{2 \sqrt[3]{2} }{ \sqrt[3]{21} }}](https://tex.z-dn.net/?f=a_4%3Da_1%2Aq%5E3%5C%5C%5C%5C+%5Cfrac%7B8%7D%7B42%7D+%3D+%5Cfrac%7B1%7D%7B4%7D%2Aq%5E3%5C%5C%5C%5C+q%5E3%3D%5Cfrac%7B%5Cfrac%7B8%7D%7B42%7D%7D%7B%5Cfrac%7B1%7D%7B4%7D%7D%5C%5C%5C%5C+q%5E3%3D%5Cfrac%7B32%7D%7B42%7D%5C%5C%5C%5C+q%5E3%3D%5Cfrac%7B16%7D%7B21%7D%5C%5C%5C%5C+%5Cboxed%7Bq%3D%5Cfrac%7B2+%5Csqrt%5B3%5D%7B2%7D+%7D%7B+%5Csqrt%5B3%5D%7B21%7D+%7D%7D "a_4=a_1*q^3\\\\ \frac{8}{42} = \frac{1}{4}*q^3\\\\ q^3=\frac{\frac{8}{42}}{\frac{1}{4}}\\\\ q^3=\frac{32}{42}\\\\ q^3=\frac{16}{21}\\\\ \boxed{q=\frac{2 \sqrt[3]{2} }{ \sqrt[3]{21} }}")
B)
C)
Respondido por
1
Resposta:
oi vc é muito linda meu anjo
Perguntas interessantes