1. Pen Tool McGraw-Hill Ryerson Pre-Calculus 11 Chapter 1 Sequences and Series Section 1.1 Click here to begin the lesson

2. Pen Tool McGraw-Hill Ryerson Pre-Calculus 11 Teacher Notes 1. This lesson is designed to help students conceptualize the main ideas of Chapter 1. 2. To view the lesson, go to Slide Show > View Show (PowerPoint 2003). 3. To use the pen tool, view Slide Show, click on the icon in the lower left of your screen and select Ball Point Pen. 4. To reveal an answer, click on or follow the instructions on the slide. To reveal a hint, click on. To view the complete solution, click on the View Solution button. Navigate through the lesson using the and buttons. 5. When you exit this lesson, do not save changes.

3. Pen Tool Sequences Complete the chart below by giving a definition, the formula for the general term and an example for each type of sequence. Chapter 1 Click here for the suggested answer. Definition of an arithmetic sequence Definition of a geometric sequence Sequences General Term Example General Term Example

4. Pen Tool Arithmetic Sequences In an arithmetic sequence, each term is found by adding a constant to the previous term. This constant is called the common difference. Chapter 1 Which of the following is an arithmetic sequence? Use the pen tool to indicate your choice by placing a in the box. 13, 26, 39, 52, 65,... 84, 72, 60, 48, 36,... 5, 11, 17, 23, 29,... 5, 10, 20, 40, 80,... 100, 80, 64, 51.2, 40.96,...

5. Pen Tool Arithmetic Sequences Nancy is cutting some ribbons into different lengths. The lengths of a group of 6 ribbons form a sequence. If the lengths of the three shortest ribbons are 15 cm, 21 cm, and 27 cm respectively. a) What is the general term of the sequence? b) What are the lengths of the three other ribbons? Chapter a) The general term of the sequence is __________________________. b) The lengths of the three other ribbons are _____________, _____________, and _____________ respectively. 1 Click here for the solution. Answer a) t n = 9 + 6n b) 33 cm, 39 cm, and 45 cm

6. Pen Tool Arithmetic Sequences Jessie is planning to train for a half marathon. The time she runs each day forms an arithmetic sequence. On the third day of the training, she ran 30 minutes. On the fifth day of the training, she ran 40 minutes. Chapter a) Determine the general term for the sequence. b) The approximate time to run a half marathon is 90 minutes. On what day of her training will Jessie run for this length of time? 1 Click here for the solution. Answer a) t n = 15 + 5n b) Fifteenth day

7. Pen Tool Arithmetic Sequences Fill in the blanks to complete the sentences, using the words below. Chapter 1 A(n) ____________________ is an ordered list of terms in which the difference between consecutive terms is constant. The constant is called the ______________________. It can be positive or negative. The _______________________ of an arithmetic sequence is t n = t 1 + (n – 1)d. nth termcommon differencearithmetic sequence Answer arithmetic sequence common difference nth term

8. Pen Tool The following pages contain solutions for the previous questions. Click here to return to the start

9. Pen Tool Solutions d = t 2 – t 1 d = 21 – 15 d = 6 Since t 1 = 15 and d = 6, the general term is t n = t 1 + (n – 1)d t n = 15 + (n – 1)6 t n = 15 + 6n – 6 t n = 9 + 6n The general term is t n = 9 + 6n. a) t 4 = 9 + 6(4) t 4 = 33 t 5 = 9 + 6(5) t 5 = 39 t 6 = 9 + 6(6) t 6 = 45 b) The lengths of the three other ribbons are 33 cm, 39 cm, and 45 cm respectively. Go back to the question

10. Pen Tool Solutions t 3 = t 1 + (3 – 1)d t 3 = t 1 + 2d 30 = t 1 + 2d t 5 = t 1 + (5 – 1)d t 5 = t 1 + 4d 40 = t 1 + 4d Subtract the two equations. 40 = t 1 + 4d 30 = t 1 + 2d 10 = 2d 5 = d Substitute d = 5 into t 3 = t 1 + 2d. 30 = t 1 + 2(5) 20 = t 1 Since t 1 = 20 and d = 5, the general term is t n = t 1 + (n – 1)d t n = 20 + (n – 1)5 t n = 20 + 5n – 5 t n = 15 + 5n a) t n = 15 + 5n 90 = 15 + 5n 15 = n Jessie will run for 90 minutes on the fifteenth day. b) Go back to the question

11. Pen Tool Solutions An ordered list of elements The difference between consecutive terms is constant. t n = t 1 + (n − 1)dt n = t 1 r n − 1 11, 18, 25,... 6, 18, 54,... Sequences Go back to the question The ratio between consecutive terms is constant.