Pregunta
Write the first five terms of the sequence. \( f(0)=-7, f(n)=3 f(n-1) \) \( f(0)=6, f(n)=-2 f(n-1) \)
Ask by Washington Deleon. in the United States
Feb 26,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
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First five terms of the first sequence:
-7, -21, -63, -189, -567
First five terms of the second sequence:
6, -12, 24, -48, 96
Solución
For the first sequence:
• f(0) = –7
• f(1) = 3(–7) = –21
• f(2) = 3(–21) = –63
• f(3) = 3(–63) = –189
• f(4) = 3(–189) = –567
For the second sequence:
• f(0) = 6
• f(1) = –2(6) = –12
• f(2) = –2(–12) = 24
• f(3) = –2(24) = –48
• f(4) = –2(–48) = 96
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Simplifique esta solución Beyond the Answer
Let's break down both sequences one by one! For the first sequence: - \( f(0) = -7 \) - \( f(1) = 3 \cdot f(0) = 3 \cdot (-7) = -21 \) - \( f(2) = 3 \cdot f(1) = 3 \cdot (-21) = -63 \) - \( f(3) = 3 \cdot f(2) = 3 \cdot (-63) = -189 \) - \( f(4) = 3 \cdot f(3) = 3 \cdot (-189) = -567 \) So the first five terms are: \(-7, -21, -63, -189, -567\). Now for the second sequence: - \( f(0) = 6 \) - \( f(1) = -2 \cdot f(0) = -2 \cdot 6 = -12 \) - \( f(2) = -2 \cdot f(1) = -2 \cdot (-12) = 24 \) - \( f(3) = -2 \cdot f(2) = -2 \cdot 24 = -48 \) - \( f(4) = -2 \cdot f(3) = -2 \cdot (-48) = 96 \) Thus, the first five terms are: \(6, -12, 24, -48, 96\).
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