Resposta:
[tex]\textsf{Leia abaixo}[/tex]
Explicação passo a passo:
[tex]\begin{cases}\mathsf{a_1 + a_2 + a_3 = 248}\\\mathsf{a_3 - a_1 = 192}\end{cases}[/tex]
[tex]\mathsf{a_1 + a_2 + (192 + a_1) = 248}[/tex]
[tex]\mathsf{2a_1 + a_2 = 56}[/tex]
[tex]\mathsf{2a_1 + a_1.q = 56}[/tex]
[tex]\mathsf{a_1(2 + q) = 56}[/tex]
[tex]\mathsf{a_1 = \dfrac{56}{2 + q}}[/tex]
[tex]\mathsf{\dfrac{56}{2 + q} + \dfrac{56.q}{2 + q} + \dfrac{56.q^2}{2 + q} = 248}[/tex]
[tex]\mathsf{56 +56.q + 56.q^2 = 496 + 248.q}[/tex]
[tex]\mathsf{56q^2 - 192q - 440 = 0}[/tex]
[tex]\mathsf{7q^2 - 24q - 55 = 0}[/tex]
[tex]\mathsf{\Delta = b^2 - 4.a.c}[/tex]
[tex]\mathsf{\Delta = (-24)^2 - 4.7.(-55)}[/tex]
[tex]\mathsf{\Delta = 576 + 1.540}[/tex]
[tex]\mathsf{\Delta = 2.116}[/tex]
[tex]\mathsf{q = \dfrac{-b \pm \sqrt{\Delta}}{2a} = \dfrac{24 \pm \sqrt{2.116}}{14} \rightarrow \begin{cases}\mathsf{q' = \dfrac{24 + 46}{14} = \dfrac{70}{14} = 5}\\\\\mathsf{q'' = \dfrac{24 - 46}{14} = -\dfrac{22}{14} = -\dfrac{11}{7}}\end{cases}}[/tex]
[tex]\boxed{\boxed{\mathsf{q = 5}}}\rightarrow\textsf{PG crescente}[/tex]
[tex]\mathsf{a_1.q^2 - a_1 = 192}[/tex]
[tex]\mathsf{a_1.(5)^2 - a_1 = 192}[/tex]
[tex]\mathsf{25a_1 - a_1 = 192}[/tex]
[tex]\mathsf{24a_1 = 192}[/tex]
[tex]\boxed{\boxed{\mathsf{a_1 = 8}}}[/tex]
[tex]\mathsf{a_2 = a_1.q}[/tex]
[tex]\mathsf{a_2 = 8.5}[/tex]
[tex]\boxed{\boxed{\mathsf{a_2 = 40}}}[/tex]
[tex]\mathsf{a_3 = a_2.q}[/tex]
[tex]\mathsf{a_3 = 40.5}[/tex]
[tex]\boxed{\boxed{\mathsf{a_3 = 200}}}[/tex]
