Question

O 7 termo de uma pg é 8 e a razao é -2 agora determine a soma dos tres primeiros termos da progressao

Answer 1

$\mathrm{a_7=8\ \ \|\ \ q=-2}\\\\ \mathrm{a_n=a_1.q^{n-1}\ \to\ a_7=a_1.q^6\ \to\ a_1=\dfrac{a_7}{q^6}}\\\\ \mathrm{a_1=\dfrac{8}{(-2)^6}=\dfrac{8}{64}\ \to\ \boxed{\mathrm{a_1=\dfrac{1}{8}}}}\\\\\\ \mathrm{S_n=a_1\bigg(\dfrac{q^n-1}{q-1}\bigg)\ \to\ S_3=\dfrac{1}{8}\bigg(\dfrac{(-2)^3-1}{-2-1}\bigg)=}\\\\\\ \mathrm{=\dfrac{1}{8}\bigg(\dfrac{-8-1}{-3}\bigg)=\dfrac{1}{8}\bigg(\dfrac{-9}{-3}\bigg)=\dfrac{1}{8}\bigg(3\bigg)}\\\\\\ \boxed{\boxed{\mathbf{S_3=\dfrac{3}{8}}}}$