# Sequences, Series, Combinations and Permutations

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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

#### Solution Summary

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.