Question

calcule a razão da p.g. onde a1=3√2 a8=48

Answer 1

$a_n=a_8=48\\ a_1=3\sqrt{2} \\ n=8\\q=?\\ \\ a_n=a_1.q^{n-1}\\ \\ 48=3\sqrt{2} .q^{8-1}\\ \\ q^7={48\over3\sqrt{2} }\\ \\ racionalisar\\ \\ q^7={48\sqrt{2} \over3\sqrt{2} .\sqrt{2} }={48\sqrt{2} \over6}\\ \\ q^7=8\sqrt{2} \\ \\ q=\sqrt[7]{8\sqrt{2}} \\ \\ q=\sqrt[7]{8\sqrt{2}} \\ \\ q=\sqrt[7]{\sqrt{2.8^2}} \\ \\ q=\sqrt[14]{128} \\ \\ q=\sqrt[14]{2^7} \\ \\ simplificando\\ \\ q=\sqrt[14:7\sqrt{x}]{2^{7:7}} \\ \\ q= \sqrt{2}$