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    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

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    https://brainmass.com/math/basic-algebra/sequences-series-combinations-permutations-30105

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