Sequences and Series

sequence that has a constant difference between consecutive terms

sum of terms in an arithmetic sequence

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.

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.

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

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

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

sequence with a limited number of terms

sum of the terms in a finite sequence

sequence that has a constant ratio between consecutive terms

sum of terms in a geometric sequence

sequence that continues without end

sum of terms in an infinite sequence

sum of a specified number of terms in a sequence

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

ordered list of numbers

sum of terms of a sequence

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."

number in a sequence