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Find the eighth term of the sequence 8,4,2

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Answer to a math question Find the eighth term of the sequence 8,4,2

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Eliseo
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Para encontrar el octavo tĂ©rmino de la secuencia, primero debemos determinar el patrĂłn de la secuencia. Examinemos la secuencia: 8, 4, 2 Observamos que cada tĂ©rmino es la mitad del tĂ©rmino anterior: \(8 \div 2 = 4\) \(4 \div 2 = 2\) Este patrĂłn indica que la secuencia es una secuencia geomĂ©trica con una razĂłn comĂșn de \( \frac{1}{2} \). Para encontrar el octavo tĂ©rmino, podemos usar la fĂłrmula para el \(n\)Ă©simo tĂ©rmino de una secuencia geomĂ©trica: \[ a_n = a_1 \times r^{(n-1)} \] DĂłnde: - \( a_n \) es el \(n\)Ă©simo tĂ©rmino, - \( a_1 \) es el primer tĂ©rmino, - \( r \) es la razĂłn comĂșn, y - \( n \) es el nĂșmero del tĂ©rmino. Para esta secuencia: - \( a_1 = 8 \) (el primer tĂ©rmino) - \( r = \frac{1}{2} \) (la razĂłn comĂșn) - \( n = 8 \) (el nĂșmero de tĂ©rmino que nos interesa) Inserte estos valores en la fĂłrmula: \[ a_8 = 8 \times \left(\frac{1}{2}\right)^{(8-1)} \] \[ a_8 = 8 \times \left(\frac{1}{2}\right)^{7} \] \[ a_8 = 8 \times \left(\frac{1}{128}\right) \] \[ a_8 = \frac{8}{128} \] \[ a_8 = \frac{1}{16} \] Entonces, el octavo tĂ©rmino de la secuencia es \( \frac{1}{16} \).

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