1. U SING AND W RITING S EQUENCES The numbers (outputs) of a sequence are called terms. sequence 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.)

2. The domain gives the relative position of each term. 1 2 3 4 5 DOMAIN: 3 6 9 12 15 RANGE: The range gives the terms of the sequence. This is a finite sequence having the rule a n = 3n, where a n represents the n th term of the sequence. U SING AND W RITING S EQUENCES n anan

3. Writing Terms of Sequences Write the first six terms of the sequence a n = 2n + 3. S OLUTION a 1 = 2(1) + 3 = 5 1st term 2nd term 3rd term 4th term 6th term a 2 = 2(2) + 3 = 7 a 3 = 2(3) + 3 = 9 a 4 = 2(4) + 3 = 11 a 5 = 2(5) + 3 = 13 a 6 = 2(6) + 3 = 15 5th term

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

5. 3 + 6 + 9 + 12 + 15 = ∑ 3i 5 i = 1 SUMMATIONSIGMA SUMMATION Notation (aka SIGMA Notation) 5 i = 1 ∑ 3i3i Is read as “the sum of 3i from i equals 1 to 5.” index of summationlower limit of summation upper limit of summation

6. SUMMATIONSIGMA SUMMATION Notation (aka SIGMA Notation) i 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 Write this series using summation notation: 5 + 10 + 15 + + 100... S OLUTION 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 terms of the series can be written as: a i = 5i where i = 1, 2, 3,..., 20 The summation notation is:

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