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Determine if the sequence is geometric. If it is, find the common ratio, the 8th term, and the explicit formula.

-4, 12, -36, 108, ..."

User FeRtoll
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Final answer:

Yes, the sequence is geometric with a common ratio of -1/3. The 8th term of the sequence is -2/1093, and the explicit formula is an = -4 * (-1/3)(n-1).

Step-by-step explanation:

Yes, the sequence is geometric. To determine the common ratio, we need to find the ratio of any two consecutive terms. Let's take the ratio of the second term (-4) to the first term (12): -4/12 = -1/3. Therefore, the common ratio is -1/3.

To find the 8th term, we can use the formula for a geometric sequence: an = a1 * r(n-1). Plugging in the values, we have: a8 = -4 * (-1/3)(8-1) = -4 * (-1/3)7 = -4 * (1/2187) = -4/2187 = -2/1093.

The explicit formula for a geometric sequence is an = a1 * r(n-1), where an represents the n-th term, a1 is the first term, and r is the common ratio. For this sequence, the explicit formula is an = -4 * (-1/3)(n-1).

User Dnyanarth Lonkar
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