Recursive Formula

A recursive formula defines the terms of a sequence using previous terms. It specifies the first term and a rule for finding subsequent terms.

The explicit formula for an arithmetic sequence is given by $$a_n = a_1 + (n-1)d$$ , where $$a_1$$ is the first term and $$d$$ is the common difference.

The explicit formula for a geometric sequence is given by $$a_n = a_1 \times r^{(n-1)}$$ , where $$a_1$$ is the first term and $$r$$ is the common ratio.

A sequence is arithmetic if the difference between consecutive terms is constant.

A sequence is geometric if the ratio of consecutive terms is constant.

The first term is defined as $$u_1 = 15$$ .

The common difference is -4.

The recursive formula is $$u_1 = 15$$ and $$u_n = u_{n-1} - 3$$ .

Substituting n=5 gives $$a_5 = 3 \times 2^{(5-1)} = 48$$ .

The explicit formula is $$a_n = -3 - 30(n - 1)$$ .