[b] Desmos Sequences

A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio.

The nth term of a geometric sequence can be found using the formula: $$a_n = a_1 \times r^{(n-1)}$$ , where $$a_1$$ is the first term and $$r$$ is the common ratio.

The common ratio is $$r = 4$$ , since each term is obtained by multiplying the previous term by -4.

The formula is $$a_n = -4 \times 4^{(n-1)}$$ .

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant, known as the common difference.

The nth term of an arithmetic sequence can be found using the formula: $$a_n = a_1 + (n-1)d$$ , where $$a_1$$ is the first term and $$d$$ is the common difference.

The common difference is $$d = 3$$ , since each term is obtained by adding 3 to the previous term.

The formula is $$a_n = 2 + (n-1) \times 3$$ .

The first term is crucial as it serves as the starting point for generating all subsequent terms in the sequence.

In mathematics, a sequence is an ordered list of numbers, where each number is called a term.