College Algebra, 2013a

658 Sequences and the Binomial Theorem
9.1.1 Exercises
In Exercises 1 - 13, write out the first four terms of the given sequence.
1. a n =2 n − 1, n ≥ 0
2. d j =(−1) j(j+1)
2 , j ≥ 1
3. {5k − 2} ∞ k=1
4.
{ } x
n ∞
5.
n 2 6.
n=1
{ n 2 ∞ n +1}
n=0
{ ln(n)
n
} ∞
n=1
7. a 1 =3,a n+1 = a n − 1, n ≥ 1 8. d 0 = 12, d m = d m-1
100 , m ≥ 1
9. b 1 =2,b k+1
=3b k +1,k ≥ 1 10. c 0 = −2, c j =
c j-1
(j +1)(j +2) , j ≥ 1
11. a 1 = 117, a n+1
= 1 , n ≥ 1 12. s 0 =1,s n+1
= x n+1 + s n , n ≥ 0
a n
13. F 0 =1,F 1 =1,F n = F n-1 + F n-2, n ≥ 2 (This is the famous Fibonacci Sequence )
In Exercises 14 - 21 determine if the given sequence is arithmetic, geometric or neither. If it is
arithmetic, find the common difference d; if it is geometric, find the common ratio r.
14. {3n − 5} ∞ n=1
15. a n = n 2 +3n +2,n ≥ 1
{
1
16.
3 , 1 ( ) }
6 , 1
12 , 1
1 n−1 ∞
24 , ... 17. 3
5
n=1
18. 17, 5, −7, −19, . . . 19. 2, 22, 222, 2222, . . .
20. 0.9, 9, 90, 900, . . . 21. a n = n!
2 , n ≥ 0.
In Exercises 22 - 30, find an explicit formula for the n th term of the given sequence.
formulas in Equation 9.1 as needed.
Use the
22. 3, 5, 7, 9, . . . 23. 1, − 1 2 , 1 4 , −1 8 , . . . 24. 1, 2 3 , 4 5 , 8 7 , ...
25. 1, 2 3 , 1 3 , 4
27 , . . . 26. 1, 1 4 , 1 9 , 1
, ... 27. x, −x3
16 3 , x5
5 , −x7 7 , ...