geometric sequence final.pptx Sequence and patterns

geometric sequence final.pptx Sequence and patterns

1. Welcome to Week 5 1

2. Practice 3 3 = _____ 2 6 = _____ 13 2 = _____ 2 3 = _____ = _____   -2 4 = _____ 5 5 = _____   27 169 8 64 3125 16 12 5

3. L et΄s have a recall ARITHMETIC SEQUENCE An arithmetic sequence is a sequence obtained by adding a common difference (𝒅) to a preceding term in order to obtain the next term. 3 2, 10, 18, 26…

4. 4 Lesson 7 GEOMETRIC Sequence

5. GEOMETRIC sequence a sequence obtained by multiplying a common ratio to the preceding terms in order to obtain the succeeding terms. 2, 16, 128, 1024…

6. formulas Common ratio r =   Nth term a n  = a 1 r n-1

7. 7 r = = =   Finding the Common ratio 2, 10, 50, 250… 3, -3, 3, -3… r = = =   1 , , , …   r = =  

8. 8 WRITING TERMS OF A GEOMETRIC SEQUENCE GIVEN 1 ST TERM AND COMMON RATIO Write the first five terms of the geometric sequence with first term 5 and common ratio 2. First term: 5 2nd term: 5(2)= 10 3rd term: 10(2)= 20 4th term: 20(2)= 40 5th term: 40(2)= 80 5, 10, 20, 40, 80

9. 9 Finding a specific term of geometric sequence Find -6, 3, , ,…   a 10  = (-6) 10-1   a n  = a 1 r n-1 a 10  = (-6) 9   a 10  = (-6)   a 10  =  

10. 10 Finding which term is an element of a geometric sequence In the G.S. 1, 3, 9, 27,… which term is 19,683? Solution: 1, 3, 9, 27,… r = = 3; a 1 =1; a n =19683 19683 = 1(3) n-1 19683 = 3 n-1 3 9 = 3 n-1 9 = n-1 n = 10   19,683 is the 10 th term

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12. DRILL 12

13. 13 1) Find the first five terms of the sequence whose first term is 9, common ratio is 3. First term: 9 2nd term: 9(3)= 27 3rd term: 27(3)= 81 4th term: 81(3)= 243 5th term: 243(3)= 729 9, 27, 81, 243, 729 Answer:

14. 14 2) Find the first four terms of the sequence whose first term is -15, common ratio is -1/3. First term: -15 2nd term: -15( )= = 5   3rd term: 5( )= -   4th term: ( )=   5th term: ( )=   -15, 5, - , , -   Answer:

15. 15 Find a 9 of geometric sequence 15, 45, 135, 405,… r = =   a 9  = (15) 9-1   a n  = a 1 r n-1 a 9  = (15) 8   a 9  = (15)   a 9  =  

16. 16 In the G.S. -2, 6, -18, 54,… which term is -13122? Solution: -2, 6, -18, 54 ,… r = = -3; a 1 =-2; a n =-13122 -13122 = -2(3) n-1 6561 = 3 n-1 3 8 = 3 n-1 8 = n-1 8 + 1 = n or n = 9   -13122 is the 9 th term

17. 17 r = = =   Finding the Common ratio r = = = x   -7, 14, -28, 56,… r = = -   6, 2 , , , …   3 , , , , …  

18. Thanks! Any questions? 📌 18

19. 19 asSIGNMENT

20. 20 ACTIVITY Find the first five terms of the sequence whose first term is 9, common ratio is 3. 2) Find the first four terms of the sequence whose first term is -15, common ratio is -1/3. Find a 9 of geometric sequence 15, 45, 135, 405,… In the G.S. -2, 6, -18, 54,… which term is -13122? Find two geometric means between 2 and 250.

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