Unit 2 Geometric Sequences and Series

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 common ratio is the factor by which we multiply each term to get the next term in the sequence.

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, $$r$$ is the common ratio, and $$n$$ is the term number.

The sum of the first n terms of a geometric series is given by: $$S_n = a_1 \times \frac{1 - r^n}{1 - r}$$ , where $$a_1$$ is the first term and $$r$$ is the common ratio.

A geometric sequence is a list of numbers, while a geometric series is the sum of the terms of a geometric sequence.

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

The 5th term is 486.

The 4th term is 108.

The sum is 31.

The common ratio is 3.