Question

Se for inserido 5 meios geométricos entre 1 e 729, nessa ordem. Qual será o 4º termo desta P.G?
a) 3
b) 6
c) 9
d) 27
e) 81​

Answer 1

$\Large\boxed{\begin{array}{l}\sf a~referida~PG~ter\acute a~7~termos\\\sf pois~s\tilde ao~5~meios~mais~os~n\acute umeros~1~e~729.\\\sf Vamos~descobrir~a~raz\tilde ao:\\\sf a_7=a_1\cdot q^6\\\sf 729=1\cdot q^6\\\sf q^6=729\\\sf q=\sqrt[\sf6]{\sf729}\\\sf q=\sqrt[\sf6]{\sf 3^6}\\\sf q=3\\\sf o~quarto~termo~ser\acute a\\\sf a_4=a_1\cdot q^3\\\sf a_4=1\cdot3^4\\\sf a_4=81\\\huge\boxed{\boxed{\boxed{\boxed{\sf\maltese~alternativa~e}}}}\end{array}}$