Question

05. (UNIFEL-MG-2009) Considere uma progressão geométrica
(P.G.) de 8 termos, em que a soma dos termos de ordem
par é 510 e a soma dos termos de ordem impar é 255.
Então, a razão q dessa P.G. vale
a) 1/3 b) 1/2 c) 2 d) 3​

Answer 1

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☞ c) A razão desta P.G. é de 2. ✅

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$\green{\rm\underline{EXPLICAC_{\!\!\!,}\tilde{A}O~PASSO{-}A{-}PASSO~~~}}$✍

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☔ Oi, Ludy. Consideremos inicialmente a soma dos termos ímpares:

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$\Large\blue{\sf a_1 + a_3 + a_5 + a_7 = 255 }$

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$\large\blue{\sf a_1 + a_1 \cdot q^2 + a_1 \cdot q^4 + a_1 \cdot q^6 = 255 }$

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$\Large\blue{\sf a_1 \cdot (1 + q^2 + q^4 + q^6) = 255 }$

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☔ Consideremos agora a soma dos termos ímpares:

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$\Large\blue{\sf a_2 + a_4 + a_6 + a_8 = 510 }$

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$\large\blue{\sf a_1 \cdot q + a_1 \cdot q^3 + a_1 \cdot q^5 + a_1 \cdot q^7 = 510 }$

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$\Large\blue{\sf a_1 \cdot (q + q^3 + q^5 + q^7) = 510 }$

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$\large\blue{\sf q \cdot \overbrace{\sf a_1 \cdot (1 + q^2 + q^4 + q^6)}^{255} = 510 }$

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$\LARGE\blue{\sf q \cdot 255 = 510 }$

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$\LARGE\blue{\sf q = \dfrac{510}{255} }$

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$\LARGE\blue{\sf q = 2 }$

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$\huge\green{\boxed{\rm~~~\red{c)}~\blue{ 2 }~~~}}$ ✅

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$\bf\large\red{\underline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}}$☁

☕ $\bf\Large\blue{Bons\ estudos.}$

($\orange{D\acute{u}vidas\ nos\ coment\acute{a}rios}$) ☄

$\bf\large\red{\underline{\qquad \qquad \qquad \qquad \qquad \qquad \quad }}\LaTeX$✍

❄☃ $\sf(\gray{+}~\red{cores}~\blue{com}~\pink{o}~\orange{App}~\green{Brainly})$ ☘☀

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$\gray{"Absque~sudore~et~labore~nullum~opus~perfectum~est."}$