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Sequences, Series, Combinations and Permutations

Please see the attached file for the fully formatted problems.

1. Write the first four terms of the sequence an = 64(1/4)n , for n=0, 1, 2, 3,...

a) 16, 4, 1, ¼
b) 60, 56, 52, 48
c) 64, 16, 4, 1
d) 256, 1024, 16384, 262144

2. Write the given series in expanded form without summation notation.

a) -x2-x3-x4-x5
b)
c)
d) -x2+x3-x4+x5

3. Find the general term an of a sequence whose first four terms are given:
5, 9, 13, 17,... for n = 1, 2, 3, 4, ...

a) an = 5n
b) an = 4n+1
c) an = 5n-2
d) an = 5n-3

4. Write the first four terms of the sequence a1 = -3, an = (-2)an-1; n = 2, 3, 4, ...

a) -3, -5, -7, -9
b) -3, 6, -12, -24
c) -3, 6, -12, 24
d) -3, -1, 1, 3
5. Determine which of the following can be the first three terms of a geometric sequence.

a) 3, -3, -3, ...
b) -8, -16, -32, ...
c) 26, 30, 34, ...
d) ½, ¼, 1/16, ...

6. Determine which of the following can be the first three terms of an Arithmetic sequence.

a) ½, ¼, 1/8, ...
b) -8, -16, -32, ...
c) -42, -37, -32, ...
d) 4, -1, 6, ...

7. Find a6 for an = 8(1/2)n, n = 1, 2, 3, 4, ...

a) 2-3
b) 1/4
c) 1/16
d) 1/32

8. Find a8 if a1 = -21, an = an-1-3; for n = 2, 3, 4, ...

a) -43
b) -42
c) -45
d) -39

9. Find if an = 27(1/3)n, n = 1, 2, 3, 4, ...

a) 9
b) 6
c) 27/2
d) 27
10. Find the sum .

a) 98
b) 153
c) 185
d) 124

11. ... = ?

a) 32/3
b) 2/5
c) 32/5
d) 2/3

12. Find if Sn =

a) 7
b) 1/7
c) 5/24
d) 2/15

13. In an arithmetic sequence, a1 =23 and a8 = 44. Find the fifth term a5.

a) 35
b) 40
c) 29
d) 36

14. Write as a fraction in lowest terms.

a) 4/5
b) 16/18
c) 8/9
d) 7/9

15. Evaluate .

a) 420
b) 210
c) 21!/(19*2)!
d) 21/38

16. Evaluate

a) 0
b) undefined
c) 4830
d) 328440

17. Find the ninth term in the expansion of (3a-b)12

a) -5940a3b9
b) 5940a3b9
c) 40,095a4b8
d) -40,095a4b8

18. Expand (x+2i)4 using the binomial formula, where i= is the imaginary unit.

a) x4+16
b) x4 +8ix3 +24x2 +32ix +16
c) x4 +8ix3 -24x2 -32ix +16
d) x4 -8ix3 +24x2 -32ix +16

19. The executive committee of the student government consists of 10 members. In how many ways can a chair, vice-chair, secretary, and a treasure be chosen, assuming one person cannot hold more than one position?

a) 151,200
b) 6
c) 5040
d) 210

20. The executive committee of the student government consists of 10 members. In how many ways can a subcommittee of 3 members be chosen?

a) 1000
b) 3
c) 720
d) 120

21. Each of three colleges sent one male and one female student to a conference. How many ways can the 6 students be seated in a row of 6 chairs if the students can sit in any order?

a) 12
b) 15
c) 30
d) 720

22. Each of three colleges sent one male and one female student to a conference. How many ways can the 6 students be seated in a row of 6 chairs if students from the same school must be seated next to each other?

a) 12
b) 15
c) 30
d) 720

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20 Algebra Problems involving Sequences, Series, Combinations and Permutations are solved. The solution is detailed and well presented. The solution received a rating of "5" from the student who posted the question.

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