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Exercise Set 6.1: Sequences & Arithmetic Sequences Write the first five terms of the following sequences. 1. an = 2n + 5...

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Exercise Set 6.1: Sequences & Arithmetic Sequences Write the first five terms of the following sequences. 1. an = 2n + 5

16.

1 2

,

2 3

,

3 4

,

4 5

,

5 6

,…

17.

9 2

,

8 3

,

7 4

,

6 5

,

5 6

,…

18. 2, 4, 8, 16, 32, …

2. bn = 3n − 2

19. 1, 3, 9, 27, 81, … 3. bn = 2

n

Determine whether the sequence is arithmetic. If the sequence is arithmetic, find the common difference.

4. an = 3n

" 1% 5. an = $ − ' # 3& " 1% 6. bn = $ − ' # 2&

n

20. 10, 8, 6, 4, 2, … 21. 4, 9, 14, 19, 24, …

n

22. 3, 2.5, 2, 1.5, 1, … 23. –24, –16, –8, 0, 8, …

7. bn =

n +1 n

8. an =

n n +1

24.

11. 1, 4, 7, 10, 13, … 12. 0, 3, 8, 15, 24, … 13. 2, 5, 10, 17, 26, …

15. 1,

1 4

1 4

,

4 3

,

8 3

,

16 3

,…

26. 3.7, 4.3, 4.9, 5.5, 6.1, …

10. 3, 7, 11, 15, 19, …

,

2 3

25. 0, ln2, ln3, ln4, ln5, …

9. 2, 5, 8, 11, 14, …

14.

,

2

Write an expression for the apparent nth term of the given sequence where n begins with 1.

1 2

1 3

,

,

,

1 8

1 9

,

,

1 16

1 16

,

1 32

1 25

,… ,…

27. 1, 4, 9, 16, 25, … Find the sum of the arithmetic sequence. 28. 2 + 4 + 6 + 8 + 10 + 12 + 14 + 16 + 18 29. 1 + 4 + 7 + 10 + 13 + 16 + 19 30. –1 + –3 + –5 + –7 + –9 + –11 + –13 31. –5 + –3 + –1 + 1 + 3 + 5 32. Sum of the first 40 positive odd integers 33. Sum of the first 100 positive even integers 34. Sum of the integers –50 to 30 35. Sum of the integers from –10 to 40