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20 terms

Sequences Vocabulary

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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)