Algebra and Trigonometry, 2015a

1076 CHAPTER 13 SEQUENCES, PROBABILITY AND COUNTING THEORY
13.2 SECTION EXERCISES
VERBAL
1. What is an arithmetic sequence? 2. How is the common difference of an arithmetic
sequence found?
3. How do we determine whether a sequence is
arithmetic?
5. Describe how linear functions and arithmetic
sequences are similar. How are they different?
4. What are the main differences between using a
recursive formula and using an explicit formula to
describe an arithmetic sequence?
ALGEBRAIC
For the following exercises, find the common difference for the arithmetic sequence provided.
6. {5, 11, 17, 23, 29, ... } 7. { 0, 1 __
2 , 1, 3 __
2 , 2, ... }
For the following exercises, determine whether the sequence is arithmetic. If so find the common difference.
8. {11.4, 9.3, 7.2, 5.1, 3, ... } 9. {4, 16, 64, 256, 1024, ... }
For the following exercises, write the first five terms of the arithmetic sequence given the first term and common
difference.
10. a 1
= −25, d = −9 11. a 1
= 0, d =
__ 2 3
For the following exercises, write the first five terms of the arithmetic series given two terms.
12. a 1
= 17, a 7
= −31 13. a 13
= −60, a 33
= −160
For the following exercises, find the specified term for the arithmetic sequence given the first term and common
difference.
14. First term is 3, common difference is 4, find the 15. First term is 4, common difference is 5, find the
5 th term.
16. First term is 5, common difference is 6, find the
8 th term.
18. First term is 7, common difference is 8, find the
7 th term.
4 th term.
17. First term is 6, common difference is 7, find the
6 th term.
For the following exercises, find the first term given two terms from an arithmetic sequence.
19. Find the first term or a 1
of an arithmetic sequence if
a 6
= 12 and a 14
= 28.
21. Find the first term or a 1
of an arithmetic sequence if
a 8
= 40 and a 23
= 115.
23. Find the first term or a 1
of an arithmetic sequence if
a 11
= 11 and a 21
= 16.
20. Find the first term or a 1
of an arithmetic sequence if
a 7
= 21 and a 15
= 42.
22. Find the first term or a 1
of an arithmetic sequence if
a 9
= 54 and a 17
= 102.
For the following exercises, find the specified term given two terms from an arithmetic sequence.
24. a 1
= 33 and a 7
= −15. Find a 4
. 25. a 3
= −17.1 and a 10
= −15.7. Find a 21
.
For the following exercises, use the recursive formula to write the first five terms of the arithmetic sequence.
26. a 1
= 39; a n
= a n − 1
−3 27. a 1
= −19; a n
= a n − 1
−1.4