Final answer:
To find the first term, plug in n=1. To find the eighth term, plug in n=8. The common ratio can be found by dividing any term by its previous term.
Step-by-step explanation:
To find the first term, the eighth term, and the common ratio of the given geometric sequence with the explicit formula aₙ= -3 (-2)ⁿ⁻¹, we need to substitute the values of n into the formula.
For the first term, plug in n=1: a₁ = -3 (-2)⁰ = -3 (1) = -3.
To find the eighth term, plug in n=8: a₈ = -3 (-2)⁸⁻¹ = -3 (-2)⁷ = -3 (-128) = -384.
The common ratio can be found by dividing any term by its previous term. For example, dividing the second term (-6) by the first term (-3) gives a common ratio of 2. So, the common ratio is 2.