# Sequences and Series

## Vocabulary

### arithmetic sequence

sequence that has a constant difference between consecutive terms

### arithmetic series

sum of terms in an arithmetic sequence

### common difference

number that is the difference between consecutive terms in an arithmetic sequence. The difference between a term and the previous term is always the same value.

### common ratio

number that is the ratio between consecutive terms in a geometric sequence. The ratio between a term and the previous term is always the same value.

### convergent series

series in which the sequence of partial sums approaches a fixed number

### divergent series

series in which the sequence of partial sums does not approach a fixed number

### explicit rule

rule used to find any term in a sequence directly, given its position in the sequence

### Fibonacci sequence

sequence of numbers in which each term is found by adding the two previous terms. The first several terms of the sequence are 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, ….

### finite sequence

sequence with a limited number of terms

### finite series

sum of the terms in a finite sequence

### geometric sequence

sequence that has a constant ratio between consecutive terms

### geometric series

sum of terms in a geometric sequence

### infinite sequence

sequence that continues without end

### infinite series

sum of terms in an infinite sequence

### partial sum

sum of a specified number of terms in a sequence

### recursive rule

rule that tells how to find any term in a sequence by using the previous term

### sequence

ordered list of numbers

### series

sum of terms of a sequence

### summation notation

abbreviated way of writing a sum that uses the Greek letter sigma. $\sum_{n=1}^{9}a_n$ is read as "the sum of $a$ sub $n$ as $n$ goes from 1 to 9."

### term of a sequence

number in a sequence