20 terms

Sequence

list of numbers written in an explicit order

arithmetic sequence

a sequence in which the same number is added between terms

geometric sequence

a sequence in which the same number is multiplied between terms

common difference

the number that is added in an arithmetic sequence, d

common ratio

the number that is multiplied in a geometric sequence, r

explicit formula for arithmetic sequence

a(n) = a + d(n-1)

explicit formula for geometric sequence

a(n) = a*r^(n-1)

recursive formula for arithmetic sequence

a(n) = previous term + d

recursive formula for geometric sequence

a(n) = previous term * r

Convergent sequence

a sequence in which there is a point when the terms of the sequence remain the same

Divergent sequence

a sequence in which the terms continue to change

Finite sequence

A sequence that has a beginning and an end

Infinite sequence

A sequence that has a beginning, but no end

explicit formula

formula to find any term in a sequence given the term number, n

recursive formula

formula to find any term in a sequence given the previous term, a(n-1)

alternating sequence

a sequence in which the sign of each term is opposite that of the previous term

series

sum of the numbers in a sequence

Infinite geometric series converge if...

|r| < 1

A convergent geometric series converges to...

a / (1 - r)

first term in a sequence

a (or a sub 1)