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B.Sc Mathematics Sequences, Probability and Counting Theory — practice questions

Explore 92 free Sequences, Probability and Counting Theory questions in B.Sc Mathematics Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Sequences, Probability and Counting Theory questions and exercises with answers

Showing questions 1–30 of 92.

Sort each sequence by its patternRead the answer and worked solution →Fill in the three series formulasRead the answer and worked solution →Match each probability termRead the answer and worked solution →Sort: permutation or combination?Read the answer and worked solution →Tap the larger countRead the answer and worked solution →Pick the right count fastRead the answer and worked solution →Order the terms of (x + y)^5Read the answer and worked solution →Find the sequence that is not arithmeticRead the answer and worked solution →True or false: chance and seriesRead the answer and worked solution →A sequence is treated as a function. What is the domain of that function?Read the answer and worked solution →What name is given to each individual number that appears in a sequence?Read the answer and worked solution →A website's daily hits double each day and the model gives a_n = 2^n. How many hits does the model predict on day 31?Read the answer and worked solution →Write the first five terms of the sequence defined by the explicit formula a_n = -3n + 8.Read the answer and worked solution →In an explicit formula, which feature makes the terms of a sequence alternate in sign?Read the answer and worked solution →A sequence is defined by a_n = n^2 when n is not divisible by 3, and a_n = n/3 when n is divisible by 3. What are its first six terms?Read the answer and worked solution →Write an explicit formula for the nth term of the sequence -2/11, 3/13, -4/15, 5/17, -6/19.Read the answer and worked solution →Each term of the Fibonacci sequence is the sum of the two preceding terms. If the eighth term is 21 and the ninth is 34, what is the tenth term?Read the answer and worked solution →What two parts must every recursive formula supply?Read the answer and worked solution →A sequence has a_1 = 9 and a_n = 3a_(n-1) - 20 for n >= 2. What is its fifth term?Read the answer and worked solution →A sequence has a_1 = 1, a_2 = 2 and a_n = 3a_(n-1) + 4a_(n-2) for n >= 3. What is its sixth term?Read the answer and worked solution →What value is assigned to zero factorial?Read the answer and worked solution →Which relation lets 5! be rewritten as 5 times 4!?Read the answer and worked solution →Why can a calculator fail to return a value for a large factorial?Read the answer and worked solution →A sequence is defined by a_n = 5n / (n + 2)!. What is its third term?Read the answer and worked solution →What property makes a sequence arithmetic?Read the answer and worked solution →Once a sequence is known to be arithmetic, how much subtraction is needed to find the common difference?Read the answer and worked solution →What does the graph of an arithmetic sequence always look like?Read the answer and worked solution →Write the first five terms of the arithmetic sequence with first term 17 and common difference -3.Read the answer and worked solution →An arithmetic sequence has first term 8 and fourth term 14. What is its fifth term?Read the answer and worked solution →Write a recursive formula for the arithmetic sequence -18, -7, 4, 15, 26.Read the answer and worked solution →

Worked practice questions

Sort each sequence by its pattern

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Left
Arithmetic
Items
  1. Item
    3, 7, 11, 15
    Answer
    Arithmetic
  2. Item
    2, 6, 18, 54
    Answer
    Geometric
  3. Item
    5, -10, 20, -40
    Answer
    Geometric
  4. Item
    17, 14, 11, 8
    Answer
    Arithmetic
  5. Item
    2, 12, 22, 32
    Answer
    Arithmetic
  6. Item
    18, 36, 72, 144
    Answer
    Geometric
  7. Item
    -18, -7, 4, 15
    Answer
    Arithmetic
  8. Item
    48, 24, 12, 6
    Answer
    Geometric
Right
Geometric
Instructions
Swipe left for a common difference, right for a common ratio.
_Source: OpenStax Algebra and Trigonometry, section 13.2 Arithmetic Sequences_

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Fill in the three series formulas

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Missing parts
  1. Answer
    n(a_1 + a_n)/2
    Choices
    1. n(a_1 + a_n)
    2. (a_1 + a_n)/2
    3. n(a_1 + a_n)/2
  2. Answer
    a_1(1 - r^n)/(1 - r)
    Choices
    1. a_1(1 - r^n)/(1 - r)
    2. a_1(1 - r)/(1 - r^n)
    3. a_1(1 + r^n)/(1 + r)
  3. Answer
    a_1/(1 - r)
    Choices
    1. a_1/(1 + r)
    2. a_1/(1 - r)
    3. a_1 r/(1 - r)
Complete the statement
Arithmetic sum: S_n = {0} Geometric sum: S_n = {1} Infinite geometric sum: S = {2}
Instructions
Tap a chip to fill each blank so every sum formula is correct.
_Source: OpenStax Algebra and Trigonometry, section 13.4 Series and Their Notations_

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Match each probability term

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Matching pairs
  1. Left
    Experiment
    Right
    An activity with an observable result
  2. Left
    Sample space
    Right
    All possible outcomes of an experiment
  3. Left
    Event
    Right
    Any subset of a sample space
  4. Left
    Outcomes
    Right
    The possible results of an experiment
  5. Left
    Complement
    Right
    The outcomes that are not in an event
  6. Left
    Mutually exclusive
    Right
    Two events with no outcomes in common
Instructions
Tap a term on the left, then tap the description that fits it.
_Source: OpenStax Algebra and Trigonometry, section 13.7 Probability_

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