PRE-CAL (1) SEQUENCES AND SERIES (1).pptx

math

1. Good day grade 11! 

2. Dear Lord and Father of all, Thank you for today. Thank you for ways in which you provide for us all. For Your protection and love, we thank you. Help us to focus our hearts and minds now on what we are about to learn. Inspire us by Your Holy Spirit as we listen and write. Guide us by your eternal light as we discover the world around us. We ask this in the name of Jesus. Amen. OPENING PRAYER

3. ATTENDANCE

4. MOTIVATION

5. Motivation Classifying Sequences! Determine whether each sequence is arithmetic or geometric. 1.) 6, 18, 54, 162, … 2.) 4, 10, 16, 22, … 3.) 625, 125, 25, 5, … 4.) -1296, 216, -36, 6, … Geometric Arithmetic Geometric Geometric

6. Motivation Classifying Sequences! Determine whether each sequence is arithmetic or geometric. 5.) 8.2, 8, 7.8, 7.6, … 6.) 11, 2, -7, -16, … 7.) -3, 9, -27, 81, … 8.) 36, 18, 9, 4.5, … Arithmetic Arithmetic Geometric Geometric

7. Sequence A sequence is a succession of numbers in a specific order. Each number in a sequence is called term . 3 , 5 , 7 , 9 , 11 1 st term/a 1 2 nd term/a 2   3 rd term/a 3 4 th term/a 4   5 th term/a 5

8. Finding the next term of the sequence To find the next term of the sequence, you should look for a pattern using the given terms of the sequence. Example: Find the next three terms of each sequence. a.) 25, 17, 9, ____, ____, ____ b.) 1, 4, 9, 16, ____, ____, ____ c. ) -5, 10, -15, 20 , ____, ____, ____

9. a.) In the sequence 25, 17, 9, …, the next term is 8 less than its preceding term. Hence, the next three terms are 1, -7 and -15. b.) In the sequence 1, 4, 9, 16, …, the next term is the square of the number. Hence, the next three terms are 25, 36, and 49. c. ) In the sequence -5, 10, -15, 20, …, the next term is a multiple of 5 whose signs alternate. Hence, the next three terms are -25, 30, -35.

10. Explicit Form of a Sequence A sequence can be expressed in a form in which a preceding term is not necessary to find the succeeding term. This explicit from can be used to find the term of the sequence by determining its position. It may be written in either subscript notation  , or in functional notation,  . Use the given explicit form of a sequence to write its first four terms. a.) b.) c. )  

11. What is the difference between arithmetic sequence and geometric sequence?

12. Arithmetic Sequence A sequence is a set of numbers that follow a pattern. Each number in the sequence is a term of the sequence. You find a term of an arithmetic sequence by adding a fixed number to the previous term. This fixed term is called common difference (d) .

13. Geometric Sequence We form a geometric sequence by multiplying a tern in the sequence by a fixed number to find the next term. The fixed is called the common ratio .

14. Another kind of number sequence is a geometric sequence . We form a geometric sequence by multiplying a tern in the sequence by a fixed number to find the next term. The fixed is called the common ratio .

15. Classifying Sequences! Determine whether each sequence is arithmetic or geometric. If the sequence is arithmetic, give the common difference. If geometric, give the common ratio. 1.) 6, 18, 54, 162, … 2.) 4, 10, 16, 22, … 3.) 625, 125, 25, 5, … 4.) -1296, 216, -36, 6, … Geometric 3 Arithmetic 6 Geometric 0.2 Geometric -0.167

16. 5.) 8.2, 8, 7.8, 7.6, … 6.) 11, 2, -7, -16, … 7.) -3, 9, -27, 81, … 8.) 36, 18, 9, 4.5, … Arithmetic -0.2 Arithmetic -9 Geometric -3 Geometric   Classifying Sequences! Determine whether each sequence is arithmetic or geometric. If the sequence is arithmetic, give the common difference. If geometric, give the common ratio.

17. What is a series?

18. Series A series is the sum of the terms of a sequence. Example: SEQUENCE SERIES  

19. Previous example: Use the given explicit form of a sequence to write its first four terms. a.) b.) c. ) Find the sum of the series. a.) b.) c. )  

20. Example: Suppose you save Php 20 on the first day, Php 60 on the second, Php 180 on the third day and continue to triple your money each day for 7 days. How much savings do you have after a week?

21. Dear Lord Thank you that you promise us that when two or more come together in Your name You are with us. Thank you, Lord, that you have been with us throughout this lesson. And that you are with us right now. Inspire us as we leave this place to love and serve You always. Amen. CLOSING PRAYER