Question

verificar se a sequência (-3/2,3,-6) é P.G:

Answer 1

$\mathsf{P.G~proposta:~(-\dfrac{3}{2},~3,-6)}\\\\\\\mathsf{Verificando~a~raz\~ao~entre~os~termos~a_1~e~a_2:}\\\\\\\mathsf{a_1\cdot q=a_2}\\\\\\\mathsf{-\dfrac{3}{2}\cdot q=3}\\\\\\\mathsf{-3\cdot q=3\cdot 2}\\\\\\\mathsf{-3\cdot q=6}\\\\\\\mathsf{q=-\dfrac{6}{3}}\\\\\\\fbox{ \mathsf{q=-2} }$


$\mathsf{Verificando~a~raz\~ao~entre~os~termos~a_2~e~a_3:}\\\\\\\mathsf{a_2\cdot q=a_3}\\\\\\\mathsf{3\cdot q=-6}\\\\\\\mathsf{q=-\dfrac{6}{3}}\\\\\\\fbox{ \mathsf{q=-2} }~~~~~~\Large\checkmark\\\\\\\large\textsf{A sequ\^encia \'e uma P.G visto que a raz\~ao entre seus termos}\\\large\textsf{\'e constante.}$