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GRE General Test Mathematics — practice by topic

Browse 33 questions across 2 Mathematics topics. Choose what you want to revise, then open a question to check its answer and worked solution.

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Mathematics topics

Sequences, Probability and Counting Theory (22)Descriptive Statistics (11)

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A sequence is defined by the explicit formula a_n = -3n + 8. Which term of the sequence equals -22?Read the answer and worked solution →A sequence is defined recursively by a_1 = 3 and a_n = 2a_(n-1) - 1 for n >= 2. What is the fifth term?Read the answer and worked solution →A sequence is defined by a_n = (n + 1)!. What is its fourth term?Read the answer and worked solution →In the Fibonacci sequence each term is the sum of the two preceding terms. The eighth term is 21 and the ninth term is 34. What is the eleventh term?Read the answer and worked solution →

Worked practice questions

A sequence is defined by the explicit formula a_n = -3n + 8. Which term of the sequence equals -22?

  1. The 9th term
  2. The 10th term
  3. The 8th term
  4. The 11th term
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Correct answer: B. The 10th term

1. An explicit formula gives any term directly from its position n, so set the formula equal to -22. 2. Solve -3n + 8 = -22: subtract 8 from both sides to get -3n = -30. 3. Divide by -3 to get n = 10, so the 10th term equals -22. 4. Checking n = 9 gives -19 and n = 11 gives -25, so neither neighboring position works. _Source: OpenStax Algebra and Trigonometry (CC BY 4.0), Ch 13 "Sequences, Probability and Counting Theory", section 13.1 SEQUENCES AND THEIR NOTATIONS_

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A sequence is defined recursively by a_1 = 3 and a_n = 2a_(n-1) - 1 for n >= 2. What is the fifth term?

  1. 31
  2. 17
  3. 33
  4. 35
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Correct answer: C. 33

1. A recursive rule builds each term from the one before it, starting from a_1 = 3. 2. a_2 = 2(3) - 1 = 5 and a_3 = 2(5) - 1 = 9. 3. a_4 = 2(9) - 1 = 17. 4. a_5 = 2(17) - 1 = 33. 5. Option B, 17, is the fourth term, the classic off-by-one trap when iterating a recursion. _Source: OpenStax Algebra and Trigonometry (CC BY 4.0), Ch 13 "Sequences, Probability and Counting Theory", section 13.1 SEQUENCES AND THEIR NOTATIONS_

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A sequence is defined by a_n = (n + 1)!. What is its fourth term?

  1. 120
  2. 24
  3. 720
  4. 60
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Correct answer: A. 120

1. Substitute n = 4 into the formula: a_4 = (4 + 1)! = 5!. 2. Expand the factorial: 5! = 5 x 4 x 3 x 2 x 1 = 120. 3. Option B, 24, is 4!, which comes from forgetting to add 1 to n before taking the factorial. _Source: OpenStax Algebra and Trigonometry (CC BY 4.0), Ch 13 "Sequences, Probability and Counting Theory", section 13.1 SEQUENCES AND THEIR NOTATIONS_

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