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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

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.

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• BSc , Wuhan Univ. China
• MA, Shandong Univ.
Recent Feedback
• "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
• "excellent work"
• "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
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