Find the seventh term of the arithmetic sequence in which a1 = 3 and d = 5. F 33. G 38 ... 7. Find the next two terms of the geometric sequence 567, 1...

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Chapter 10 Final Exam Review

SCORE _____________

Write the letter for the correct answer in the blank at the right of each question. 1. Find the next four terms of the arithmetic sequence 11, 15, 19, … . A 24, 29, 34, 39 C 20, 21, 22, 23 B 22, 25, 28, 31 D 23, 27, 31, 35

1. __D____

2. Find the seventh term of the arithmetic sequence in which a1 = 3 and d = 5. F 33 G 38 H 30 J 31

2. __F____

3. Find the two arithmetic means between 10 and 70. A 30, 50 B 25, 45 C 40, 40

D 28, 43

3. __A____

4. Find Sn for the arithmetic series in which a1 = 4, d = 3, and an = 61. F 20 G 1280 H 64

J 650

4. __J____

5. Find the sum of the arithmetic series 8 + 5 + 2 + (–1) + … + (–13). A1 B –20 C 50

D 29

5. __B____

J 90

6. __H____

D 9, 3

7. __B____

5

𝟔. Find ∑ (4𝑛 + 1). 𝑛=1

F 44

G 60

H 65

7. Find the next two terms of the geometric sequence 567, 189, 63 … . A 21, 3 B 21, 7 C –63, –189

8. Find the fifth term of a geometric sequence for which a3 = 20 and r = 2. F 80 G 40 H 160 J 24

8. __F____

9. Find the sum of a geometric series for which a1 = 6, an = 96, and r = 2. A 174 B 180 C 186 D 192

9. __C____

10. Find the sum of a geometric series for which a1 = 7, n = 4, and r = 3. F 91 G 280 H 147 J 189

10. __G____

4

𝟏𝟏. Find ∑ 3 · 2𝑛 − 1 . 𝑛=1

A 80

Chapter 10

B –80

D –45

C 45

57

11. __C____

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NAME _____________________________________________ DATE ____________________________ PERIOD _____________

Chapter 10 Final Exam Review (continued) 12. Find a1 in a geometric series for which Sn = 93, r = 2, and n = 5. F –3 G 15.5 H3

1

J3

12. __H____

13. Find the sum of the infinite geometric series 12 + 6 + 3 + …, if it exists. A 24 B8 C 27 D does not exist

13. __A____

̅̅̅ as a fraction. 14. Write 0. ̅48 1 16 F 48 G 3

14. __J____

12

16

H 25

J 33

15. Find the fifth term of the sequence in which a1 = 4 and an+1 = an + 6. A 5184 B 34 C 28 D 22

15. __C____

16. Find the third iterate of f(x) = 2x + 3 for an initial value of x0 = 2. F7 G 15 H 17

16. __J____

J 37

17. Expand (m + 1)3. A m3 + 3m2 + 3m + 1 B m2 + 2m + 1

C m3 + 1 D m3 + 2m2 + 2m + 1

17. __A____

18. Expand (x + 2y)3. F x3 + 6x2y + 12xy2 + 8y3 G x2 + 4xy + 4y2

H x3 + 8y3 J x3 + 4x2 y + 4xy2 + 8y3

18. __F____

19. n = 1 is a counterexample to which statement? 𝑛(𝑛 + 1) A 2 + 4 + 6 + … + 2n = n(n + 1) C1+2+3+…+n= 2 B 4n – 1 is divisible by 3. D 2n + 1 is divisible by 2.

19. __D____

20. Which is not a step in an induction proof? F Assume that the statement is true for some natural number k. G Show that the statement is true for some integer n. H Show that the statement is true for some natural number k. J Show that the statement is true for the next integer k + 1.

20. ___H___

Bonus Express the series 3 + 6 + 12 + 24 + 48 using sigma notation.

Chapter 10

58

B: ∑𝟓𝒏=𝟏 𝟑(𝟐)𝒏−𝟏

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