Final answer:
The common ratio of the sequence is 3. The first five terms are -3, -9, -27, -81, and -243. The explicit formula for the sequence is an = -3 * 3n-1.
Step-by-step explanation:
The given sequence is defined by the formula an = an-1 * 3, with a1 = -3.
To find the common ratio of this sequence, we divide any term by its previous term. Let's divide the second term by the first term:
a2 / a1 = (a1 * 3) / a1 = 3.
So, the common ratio of this sequence is 3.
The first five terms of the sequence are:
- a1 = -3
- a2 = -3 * 3 = -9
- a3 = -9 * 3 = -27
- a4 = -27 * 3 = -81
- a5 = -81 * 3 = -243
The explicit formula for this sequence can be derived by recognizing that each term is obtained by multiplying the previous term by 3. Therefore, the explicit formula is an = a1 * 3n-1.