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Determine if the sequence is geometric. If it is, find the common ratio, the 8th term? And the explicit formula from this sequence 162, -54, 18, -6,…

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Answer to a math question Determine if the sequence is geometric. If it is, find the common ratio, the 8th term? And the explicit formula from this sequence 162, -54, 18, -6,…

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Cristian
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114 Answers
1. Calculate ratio between terms:
r = \frac{-54}{162} = -\frac{1}{3}
Sequence is geometric as ratio is constant.
2. Determine explicit formula:
a_n = 162 \left( -\frac{1}{3} \right)^{n-1}
3. Find the 8th term:
a_8 = 162 \left( -\frac{1}{3} \right)^{7}
a_8 = -\frac{2}{27}
Answer: Sequence is geometric. Common ratio: -\frac{1}{3}, 8th term: -\frac{2}{27}, Explicit formula: a_n = 162 \cdot \left( -\frac{1}{3} \right)^{n-1}.

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(3b)⋅(5b^2)⋅(6b^3)

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