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9 Cards in this Set
- Front
- Back
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What is the formula of the mth term of a arithmetic sequence and state the terms |
Uₙ = a + (n - 1)d where a is the first term n is the number of terms d is the common difference |
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give the formula for the sum of an arithmetic series and state the terms |
Sₙ = ⁿ/₂ (2a + (n + 1)d) where a is the first term n is the number of terms d is the commin difference |
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state the difference between a geometric and an arithmetic sequence |
a geometric sequence has a common ratio (r) ie. 2, 4, 8, 16 an arithmetic sequence has a common difference (d) ie 2, 4, 6, 8 |
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state the formula for the nth term of an geometric sequence and define each term |
Uₙ = arⁿ⁻¹ where a is the first term r is the common ratio n is the number of terms |
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give the formulas for the sum of the first n terms of a geometric series and define each term |
Sₙ = a(1 - rⁿ) / 1 - r Sₙ = a(rⁿ - 1) / r - 1 where a is the first term r is the common difference n is the number of terms |
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what is a divergent series |
-the terms of the series are getting larger -as n tends to infinity Sₙ also tends to infinity |r|> 1 |
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what is a convergent series |
-the terms of the series are gettiny smaller -as n tends to infinity Sₙ gets closer to a finite number. - the finite number is labeled S∞ -|r|< 1 |
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which formulas give the sum of the first n terms of a geometric series |
Sₙ = a(1 - rⁿ) / 1 - r for divergent S∞ = a / 1 - r for convergent |
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what are the first 4 terms of an geometric series algebreacly |
a + ar + ar² + ar³ |
