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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 término de la secuencia, primero debemos determinar el patrón de la secuencia. Examinemos la secuencia: 8, 4, 2 Observamos que cada término es la mitad del término anterior: \(8 \div 2 = 4\) \(4 \div 2 = 2\) Este patrón indica que la secuencia es una secuencia geométrica con una razón común de \( \frac{1}{2} \). Para encontrar el octavo término, podemos usar la fórmula para el \(n\)ésimo término de una secuencia geométrica: \[ a_n = a_1 \times r^{(n-1)} \] Dónde: - \( a_n \) es el \(n\)ésimo término, - \( a_1 \) es el primer término, - \( r \) es la razón común, y - \( n \) es el número del término. Para esta secuencia: - \( a_1 = 8 \) (el primer término) - \( r = \frac{1}{2} \) (la razón común) - \( n = 8 \) (el número de término que nos interesa) Inserte estos valores en la fórmula: \[ a_8 = 8 \times \left(\frac{1}{2}\right)^{(8-1)} \] \[ a_8 = 8 \times \left(\frac{1}{2}\right)^{7} \] \[ a_8 = 8 \times \left(\frac{1}{128}\right) \] \[ a_8 = \frac{8}{128} \] \[ a_8 = \frac{1}{16} \] Entonces, el octavo término de la secuencia es \( \frac{1}{16} \).

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