a +b Hence a player's probability of winning is proportional to the amount of money a +b with which he or she starts the game. EXERCISES 9.3 In Exercises 1-24, find an explicit formula for sn if so, S1, S2, . . . is a sequence satisfying the given recurrence relation and initial conditions. 1. Sn= Sn-1 + 3, so = 2 3. Sn= 4sn-1, So 5 2. Sn 5sn-1 - 4, so 1 4. Sn= 1.5s-1 - 1, So = 4 6. Sn Sn-1- 10, So = 32 8. Sn=-2sn-1, So = -5 5. Sn=-Sn-1 +6, So = -4 7. Sn 3sn-1 - 8, so = 3 10. Sn=-Sn-1 +7, so = 1 10s-1-45, So = 2 9. Sn= Sn-1-5, So = 100 11.) Sn=-2sn-1 9, So = 7 12. Sn 11 13. Sn= Sn-1 + 2sn-2, So = 9, s1 = 0 14. Sn -2sn-1- Sn-2, S0= 3, s1 = 1 16. Sn= 4sn-2, So = -1, S1 -14 18. Sn= 6s1-1 - 9sn-2, So = 1, S1 = 9 15. Sn= 8sn-1 16s-2, So = 6, s1 20 17. Sn= 9Sn-2, SO = 1, S1 = 9 20. Sn-8sn-1 - 15sn-2, S0 = 2, S1= 2 19. Sn=-4sn-1 -4sn-2, So -4, S1 2 = -7, s1= -15 21. Sn= 10sn-1- 25s-2, So 22. Sn= 10s,-1 24s-2, S0 = 1, S1 = 0 15 24. Sn= 4Sn-1-4sn-2, So = -3, s1 = 4 www 23. Sn =-5sn-1 - 4sn-2, S0 = 3, S1 25. In order to combat hypertension, Mr. Lorenzo is to take a capsule containing 25 mg of a drug each morning after awaking. During the next 24 hours, 20 percent of the amount of the drug in the body is eliminated. Write a difference equation and initial conditions giving the amount of the drug in Mr. Lorenzo's body nmediately after he takes the nth capsule. (a)
a +b Hence a player's probability of winning is proportional to the amount of money a +b with which he or she starts the game. EXERCISES 9.3 In Exercises 1-24, find an explicit formula for sn if so, S1, S2, . . . is a sequence satisfying the given recurrence relation and initial conditions. 1. Sn= Sn-1 + 3, so = 2 3. Sn= 4sn-1, So 5 2. Sn 5sn-1 - 4, so 1 4. Sn= 1.5s-1 - 1, So = 4 6. Sn Sn-1- 10, So = 32 8. Sn=-2sn-1, So = -5 5. Sn=-Sn-1 +6, So = -4 7. Sn 3sn-1 - 8, so = 3 10. Sn=-Sn-1 +7, so = 1 10s-1-45, So = 2 9. Sn= Sn-1-5, So = 100 11.) Sn=-2sn-1 9, So = 7 12. Sn 11 13. Sn= Sn-1 + 2sn-2, So = 9, s1 = 0 14. Sn -2sn-1- Sn-2, S0= 3, s1 = 1 16. Sn= 4sn-2, So = -1, S1 -14 18. Sn= 6s1-1 - 9sn-2, So = 1, S1 = 9 15. Sn= 8sn-1 16s-2, So = 6, s1 20 17. Sn= 9Sn-2, SO = 1, S1 = 9 20. Sn-8sn-1 - 15sn-2, S0 = 2, S1= 2 19. Sn=-4sn-1 -4sn-2, So -4, S1 2 = -7, s1= -15 21. Sn= 10sn-1- 25s-2, So 22. Sn= 10s,-1 24s-2, S0 = 1, S1 = 0 15 24. Sn= 4Sn-1-4sn-2, So = -3, s1 = 4 www 23. Sn =-5sn-1 - 4sn-2, S0 = 3, S1 25. In order to combat hypertension, Mr. Lorenzo is to take a capsule containing 25 mg of a drug each morning after awaking. During the next 24 hours, 20 percent of the amount of the drug in the body is eliminated. Write a difference equation and initial conditions giving the amount of the drug in Mr. Lorenzo's body nmediately after he takes the nth capsule. (a)
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Chapter2: Second-order Linear Odes
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Transcribed Image Text:a +b
Hence a player's probability of winning is proportional to the amount of money
a +b
with which he or she starts the game.
EXERCISES 9.3
In Exercises 1-24, find an explicit formula for sn if so, S1, S2, . . . is a sequence satisfying the given recurrence
relation and initial conditions.
1. Sn= Sn-1 + 3, so = 2
3. Sn= 4sn-1, So 5
2. Sn 5sn-1 - 4, so 1
4. Sn= 1.5s-1 - 1, So = 4
6. Sn Sn-1- 10, So = 32
8. Sn=-2sn-1, So = -5
5. Sn=-Sn-1 +6, So = -4
7. Sn 3sn-1 - 8, so = 3
10. Sn=-Sn-1 +7, so = 1
10s-1-45, So
= 2
9. Sn= Sn-1-5, So = 100
11.) Sn=-2sn-1
9, So = 7
12. Sn
11
13. Sn= Sn-1 + 2sn-2, So = 9, s1 = 0
14. Sn
-2sn-1- Sn-2, S0= 3, s1 = 1
16. Sn= 4sn-2, So = -1, S1 -14
18. Sn= 6s1-1 - 9sn-2, So = 1, S1 = 9
15. Sn=
8sn-1 16s-2, So = 6, s1 20
17. Sn=
9Sn-2, SO
= 1, S1 = 9
20. Sn-8sn-1
- 15sn-2, S0 = 2, S1= 2
19. Sn=-4sn-1 -4sn-2, So -4, S1 2
= -7, s1= -15
21. Sn= 10sn-1- 25s-2, So
22. Sn=
10s,-1 24s-2, S0 = 1, S1 = 0
15
24. Sn=
4Sn-1-4sn-2, So = -3, s1 = 4
www
23. Sn =-5sn-1 - 4sn-2, S0 = 3, S1
25. In order to combat hypertension, Mr. Lorenzo is to take a capsule containing 25 mg of a drug each morning
after awaking. During the next 24 hours, 20 percent of the amount of the drug in the body is eliminated.
Write a difference equation and initial conditions giving the amount of the drug in Mr. Lorenzo's body
nmediately after he takes the nth capsule.
(a)
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