Question

calcular o valor de x na P.G (8,-6,x)

Answer 1

$\large\textsf{Progress\~ao geom\'etrica~proposta~: (8, -6, x)}\\\\\\\textsf{F\'ormula de recorr\^encia em uma P.G:}\\\\\\\fbox{ \mathsf{a_1\cdot q=a_2} }\\\\\\\mathsf{a_1=primeiro~termo;}\\\mathsf{q=raz\~ao;}\\\mathsf{a_2=segundo~termo.}\\\\\\\mathsf{8\cdot q=-6}\\\\\\\mathsf{q=-\dfrac{6}{8}}$


$\large\textsf{Substituindo:}\\\\\\\mathsf{a_2\cdot q=x}\\\\\\\mathsf{-6\cdot-\dfrac{6}{8}=x}\\\\\\\mathsf{\dfrac{36}{8}=x~~~~(simplificando...)}\\\\\\\fbox{ \mathsf{x=\dfrac{9}{2}} }$


$\textsf{\large\'E uma P.G alternante, onde cada novo termo tem sinal diferente}\\\large\textsf{do termo anterior.}$