Chapter 1 - XYZ Custom Plus

8Chapter 1 The Basicsc. For the sequence in part (c), there is no number to add each timeor multiply by each time. However, the pattern becomes apparentwhen we look at the differences between the numbers:24 7 11. . .23 4Proceeding in the same manner, we would add 5 to get the next term, giving us11 + 5 = 16.In the introduction to this chapter we mentioned the mathematician known asFibonacci. There is a special sequence in mathematics named for Fibonacci. Hereit is.Fibonacci sequence = 1, 1, 2, 3, 5, 8, . . .Can you see the relationship among the numbers in this sequence? Start with two1’s, then add two consecutive members of the sequence to get the next number.Here is a diagram.1 1 2 3 5 8Sometimes we refer to the numbers in a sequence as terms of the sequence.16. Write the first 10 terms of thefollowing sequence.2, 2, 4, 6, 10, 16, . . .Example 16Write the first 10 terms of the Fibonacci sequence.Solution The first six terms are given above. We extend the sequence by adding5 and 8 to obtain the seventh term, 13. Then we add 8 and 13 to obtain 21.Continuing in this manner, the first 10 terms in the Fibonacci sequence are1, 1, 2, 3, 5, 8, 13, 21, 34, 55Each section of the book will end with some problems and questions like the onesthat follow. They are for you to answer after you have read through the sectionbut before you go to class. All of them require that you give written responses incomplete sentences. Writing about mathematics is a valuable exercise. If youwrite with the intention of explaining and communicating what you know tosomeone else, you will find that you understand the topic you are writing abouteven better than you did before you started writing. As with all problems in thiscourse, you want to approach these writing exercises with a positive point ofview. You will get better at giving written responses to questions as you progressthrough the course. Even if you never feel comfortable writing about mathematics,just the process of attempting to do so will increase your understanding andability in mathematics.Getting Ready for ClassAfter reading through the preceding section, respond in your ownwords and in complete sentences.Answers15. a. 19 b. 81 c. 2016. 2, 2, 4, 6, 10, 16, 26, 42, 68, 1101. What is a variable?2. Write the first step in the rule for order of operations.3. What is inductive reasoning?4. Explain the relationship between an exponent and its base.