| Sequences, Series and Summations |
-- Section 8.2 -- |
| Sequence: | a function whose domain is the set of
natural numbers. natural numbers (counting numbers) {1, 2, 3, 4...} |
| Series: | is a sum of a sequence. |
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Write the first five terms of the sequence. an = 2n2 - n |
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Solve |
Step |
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a1 = 2(1)2 - 1 = 2(1) - 1 = 2 - 1 = 1 |
Start with n = 1 | |
| a2 = 2(2)2 - 2 = 2(4) - 2 = 8 - 2 = 6 | n = 2 | |
| a3 = 2(3)2 - 3 = 2(9) - 3 = 18 - 3 = 15 | n = 3 | |
| a4 = 2(4)2 - 4 = 2(16) - 4 = 32 - 4 = 28 | n = 4 | |
| a5 = 2(5)2 - 5 = 2(25) - 5 = 50 - 5 = 45 | n = 5 | |
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The first five terms are 1, 6, 15, 28, 45 |
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an = 2n2 - n can also be written as f(n) = 2n2 - n . The term an indicates it is a special function called a sequence.
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Write the first five terms of the sequence. an = n2 + 3n |
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[Solution] |
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Evaluate the sum. |
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| We add the first five terms of the sequence an = 2n2 - n from example 1. | ||
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Solve |
Step |
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| The first five terms are 1, 6, 15, 28, 45 | ||
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= 1 + 6 + 15 + 28 + 45 = 95 | n
= 1 means start at 1 5 means end at 5. |
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Evaluate the sum. |
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[Solution] |
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Evaluate the sum. |
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Solve |
Step |
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K
= 3 means
start
at 3 5 means end at 5. k = 3, 4, 5 |
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Add the fractions | |
| The sum of a sequence is called a series. | ||
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Evaluate the sum. |
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[Solution] |
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Tutorials and Applets by
Joe McDonald
Community College of Southern Nevada