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15 Cards in this Set
- Front
- Back
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What is a sequence?
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A sequence is a function whose domain is the set of natural numbers (the term numbers), and whose range is the set of term values.
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What is an arithmetic sequence?
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An arithmetic sequence is a sequence in which one term equals a constant added to the preceding term.
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What is a geometric sequence?
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A geometric sequence is a sequence in which each term equals a constant multiplied by the preceding term.
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How do you find the term-value of an arithmetic sequence?
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The nth term of an arithmetic sequence equals the first term plus (n -1) common differences. That is
tn = t1 + (n-1)d |
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How do you find the term-value of a geometric sequence?
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The nth term of a geometric sequence equals the first term multiplied by (n-1) common ratios. That is
tn = t1 * r^(n-1) |
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What are arithmetic or geometric means?
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Arithmetic or geometric means between two numbers are numbers which form arithmetic or geometric sequences with the two given numbers
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What is a series?
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A series is the indicated sum of the terms of a sequence
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How do you find the nth partial sum?
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The nth partial sum of a series is the sum of the first n terms of that series.
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What is an arithmetic or geometric series?
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An arithmetric or geometric series is a series which results from adding the terms of an arithmetic or geometric sequence, respectively.
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How do you find the partial sum of an arithmetic series?
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The partial sum of an arithmetic series is a) the sume of the first and last term, multiplied by half the number of terms, or b) n times the average of the first and last terms. That is
Sn = n/2 (t1+tn) = n[ (t1 + tn) /2 ] |
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How do you find the partial sum of a geometric series?
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The nth partial sum of a geometric series equals the first term times a fraction. The fraction is [ ( 1 - r^n) / ( 1 - r) ]. That is
Sn = t1 * [ ( 1-r^n) / (1-r) ] |
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How do you know if a series converges?
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A series converges to a number S if the partial sums, Sn, stay arbitrarily close to S as n gets very large.
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How do you know if a geometric series converges?
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A geometric series converges if | r | < 1. The limit, S, to which it converges is given by
S = limn->inf Sn = [ t1 / (1-r) ] |
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If x is a repeating decimal, the what kind of number is it?
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It x is a repeating decimal, then x is a rational number.
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What does n factorial mean?
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The expression n! (n factorial) means the product of the first consecutive positive integers.
n! = n * (n-1)! |
