Question

Determine a razão da PG cujo termo é 1/27 e o 7° é 81

Answer 1

Explicação passo-a-passo:

$Se ~~3^\circ}~~termo~~\'e~~{1\over27}\\ \\ a_3=27\\ \\ Usando ~~ a ~~forma~~geral\\ \\ a_n=a_1.q^{n-1}\\ \\ a_1.q^{3-1}={1\over27}\\ \\ a_1.q^2={1\over3^3}\\ \\ a_1.q^2=3^{-3}~~~( I )\\ ---------------------\\ a_7=81\\ \\ a_1.q^{7-1}=81\\ \\ a_1.q^6=3^4~~~( II )\\ \\ ------------------------\\ \\ dividir (II ) ~~pela~~( I )\\ \\ {a^1.q^6 \over a_1.q^2}={3^4\over3^{-3}}\\ \\ cancela~~a_1\\ \\ q^6\div q^2=3^4\div3^{-3}\\ \\ q^4=3^{4-(-3)}\\ \\ q^4=3^{4+3}\\ \\ q^4=3^7\\ \\ q=\sqrt[4]{3^7}$

$q=\sqrt[4]{3^4.3^3} \\ \\ q=3\sqrt[4]{3^3} \\ \\ q=3\sqrt[4]{27} \\ \\ logo ~~a~~ raz\tilde{a}o~~ \'e~~3\sqrt[4]{27}$