1. Write the first six terms of the following sequences.

2. Objective: (1) Using and Writing Sequences Agenda: 03/31/15 1.) Warm-up 2.) Questions: TB pg. 655 #’s 9-29 ALL (Skip #23) 3.) Lesson: 11.1 An Introduction To Sequences and Series (Continue) 4.) Class/Homework 5.) Work in Pairs STAY ON TASK!!!

3. 11.1 An Introduction to Sequences and Series (Day 2) sequence added When the terms of a sequence are added, the resulting expression is called a series. A series can be finite or infinite. 3 + 6 + 9 + 12 + 15(Finite Series) 3 + 6 + 9 + 12 + 15 + …(Infinite Series) summation notation You can use summation notation to write a series. For example, for the finite series: 3 + 6 + 9 + 12 + 15 = i1 5 i Where i is the index of the summation, 1 is the lower limit of the summation, and 5 is the upper limit of the summation. The summation notation is read “the sum from i equals 1 to 5 of 3i.” Summation notation is also called sigma notation because it uses the uppercase Greek letter sigma.

4. 11.1 An Introduction to Sequences and Series (Day 2) infinite finite Summation notation for an infinite series is similar to that for a finite series. For example, for the infinite series: 3 + 6 + 9 + 12 + 15 + … = The infinity symbol, ∞, indicates that the series continues without end. Ex. 1Write the following series with summation notation. 5 + 10 + 15 + … + 100 Notice that the first term is 5(1), the second term 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 for the series is:

5. 11.1 An Introduction to Sequences and Series (Day 2) Ex. 2Write the following series with summation notation. Notice that for each term the denominator of the fraction is 1 more than the numerator. So, the terms of the series can be written as: Where i = 1, 2, 3, 4, … The summation notation for the series is:

6. 11.1 An Introduction to Sequences and Series (Day 2) 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. Ex. 3Find the sum of the series.

7. Math Humor Q: Why do mathematicians watch so much TV? series A: They like all types of series. Math

8. 11.1 An Introduction to Sequences and Series (Day 2) three special There are formulas for finding the sum of the terms of three special types of sequences.

9. 11.1 An Introduction to Sequences and Series (Day 2) Ex. 4 Use one of the formulas for special series to find the sum of the series. We can use the SECOND formula. Substitute 100 for n. 50 1

10. 11.1 An Introduction to Sequences and Series (Day 2) YOU TRY Ex. 5YOU TRY Use one of the formulas for special series to find the sum of the series. We can use the THIRD formula. Substitute 12 for n.

11. HOMEWORK Page 655;36 - 63 ALL