Question

To find the fourth term, we can use the following recurrence formula:

d(n) = d(n-1) * (-6)
(A) 18
(B) -18
(C) 3
(D) -6

Answer 1

To find the fourth term of the sequence using the recurrence formula d(n) = d(n-1) * (-6), we must know the earlier terms. Without an initial value, we cannot determine the fourth term or choose between the given options.

Step-by-step explanation:

The question asks to find the fourth term of a sequence using the given recurrence formula d(n) = d(n-1) * (-6). To find this, we must know the first term of the sequence, since subsequent terms depend on the previous term. Assuming the first term is given to us or that we have enough prior terms to calculate the fourth term:

1. Let's denote the first term as d(1).
2. To find the second term, d(2), we apply the recurrence formula: d(2) = d(1) * (-6).
3. For the third term, d(3), we again apply the formula: d(3) = d(2) * (-6).
4. Finally, for the fourth term, d(4), we use the previous term: d(4) = d(3) * (-6). This product will give us the fourth term in the sequence, depending on the values of previous terms.

Without an initial term, we cannot determine a specific value, so we cannot choose between the provided options (A) 18, (B) -18, (C) 3, or (D) -6. Further information about the initial term of the sequence is needed to solve the problem completely.