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U SING AND W RITING S EQUENCES

U SING AND W RITING S EQUENCES. You can think of a sequence as a set of numbers written in a specific order. ( Any sequence can be defined as a function whose domain is the set of natural numbers .). The numbers (outputs) of a sequence are called terms. U SING AND W RITING S EQUENCES.

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U SING AND W RITING S EQUENCES

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  1. USING AND WRITING SEQUENCES You can think of a sequence as a set of numbers written in a specific order. (Any sequence can be defined as a function whose domain is the set of natural numbers.) The numbers (outputs) of a sequence are called terms.

  2. USING AND WRITING SEQUENCES n an 1 2 3 4 5 DOMAIN: The domain gives the relative positionof each term. The range gives the terms of the sequence. 3 6 9 12 15 RANGE: This is a finite sequence having the rule an= 3n, where anrepresents the nth term of the sequence.

  3. Writing Terms of Sequences Write the first six terms of the sequence an = 2n + 3. SOLUTION a1= 2(1) + 3 = 5 1st term a2= 2(2) + 3 = 7 2nd term a3= 2(3) + 3 = 9 3rd term a4= 2(4) + 3 = 11 4th term a5= 2(5) + 3 = 13 5th term a6= 2(6) + 3 = 15 6th term

  4. Writing Terms of Sequences Write the first six terms of the sequence f(n) = (–2)n – 1 . SOLUTION f(1) = (–2)1 – 1 = 1 1st term f(2) = (–2)2 – 1 = –2 2nd term f(3) = (–2)3 – 1 = 4 3rd term f(4) = (–2)4 – 1 = – 8 4th term f(5) = (–2)5 – 1 = 16 5th term f(6) = (–2)6 – 1 = – 32 6th term

  5. 5 ∑ 3i i= 1 5 3 + 6 + 9 + 12 + 15 = ∑3i i = 1 SUMMATION Notation (aka SIGMA Notation) Is read as “the sum of 3i from iequals 1 to 5.” upper limit of summation index of summation lower limit of summation

  6. SUMMATION Notation (aka SIGMA Notation) The index of summation does not have to be i. Any letter can be used. Also, the index does not have to begin at 1 (but often does).

  7. Writing Series with Summation Notation . . . 5 + 10 + 15 + + 100 The summation notation is: Write this series using summation notation: SOLUTION Notice that the first term is 5(1), the second is 5(2),the third is 5(3), and the last is 5(20). So the termsof the series can be written as: ai= 5i where i = 1, 2, 3, . . . , 20

  8. SOLUTION: Example: Write the series represented by the summation notation . Then find the sum.

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