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NSC / Matric Sequences and Series — practice questions

Explore 52 free Sequences and Series questions in NSC / Matric Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Sequences and Series questions and exercises with answers

Showing questions 1–30 of 52.

What makes a sequence an arithmetic sequence?Read the answer and worked solution →In a geometric sequence, how is each new term obtained from the term before it?Read the answer and worked solution →Why can an arithmetic series never converge to a finite sum?Read the answer and worked solution →A geometric series has a first term of 12 and a constant ratio of one third. What is its sum to infinity?Read the answer and worked solution →An arithmetic sequence has a first term of 7 and a common difference of 4. What is its fifteenth term?Read the answer and worked solution →Match each series word to its meaningRead the answer and worked solution →Complete the definition of conditional probabilityRead the answer and worked solution →True or false: conditional probabilityRead the answer and worked solution →Independent or mutually exclusive?Read the answer and worked solution →Match each rule to its nameRead the answer and worked solution →IndependenceRead the answer and worked solution →Order the steps for a Bayes' theorem questionRead the answer and worked solution →Complete the conditions for a partitionRead the answer and worked solution →True or false: independence versus exclusivityRead the answer and worked solution →Assertion and reasonRead the answer and worked solution →Tap every statement that follows from independenceRead the answer and worked solution →The multiplication ruleRead the answer and worked solution →Spot the one that does not belongRead the answer and worked solution →Two are true, one is notRead the answer and worked solution →Three of these are wrong. Find the one that holds.Read the answer and worked solution →Complete the theorem of total probabilityRead the answer and worked solution →Which theorem answers which question?Read the answer and worked solution →True or false: total probability and BayesRead the answer and worked solution →Match each historical figure to their contributionRead the answer and worked solution →The Historical NoteRead the answer and worked solution →Flip and pair: notation with meaningRead the answer and worked solution →Order the reasoning: from a partition to a posteriorRead the answer and worked solution →Tap every quantity that is a probabilityRead the answer and worked solution →Spot the odd one outRead the answer and worked solution →Assertion and reason: the multiplication ruleRead the answer and worked solution →

Worked practice questions

What makes a sequence an arithmetic sequence?

  1. A constant is added each time
  2. A constant is used to multiply
  3. The terms are always positive
  4. The terms always get larger
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Correct answer: A. A constant is added each time

1. Take any term of the sequence and look at how the next one is produced from it. 2. In an arithmetic sequence the same constant is added each time, and that constant is the common difference. 3. The constant may be negative, in which case the terms fall rather than rise. 4. Multiplying by a constant instead would build a geometric sequence. _Source: Siyavula Mathematics Grade 12 (Everything Maths, CC BY 4.0), Chapter 1: Sequences and series_

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In a geometric sequence, how is each new term obtained from the term before it?

  1. It has a constant added to it
  2. It is multiplied by a constant
  3. It is squared every single time
  4. It is halved every single time
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Correct answer: B. It is multiplied by a constant

1. A geometric sequence grows or shrinks by the same factor at every step. 2. That factor is found by dividing any term by the term before it, and it is called the constant ratio. 3. So each new term is the previous term multiplied by that constant ratio. 4. Halving is only one special case of this, with a ratio of one half. _Source: Siyavula Mathematics Grade 12 (Everything Maths, CC BY 4.0), Chapter 1: Sequences and series_

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Why can an arithmetic series never converge to a finite sum?

  1. Its terms are always positive
  2. Its first term is always one
  3. Its sum runs off to infinity
  4. Its common difference is zero
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Correct answer: C. Its sum runs off to infinity

1. A series converges when its running total settles closer and closer to one fixed value. 2. In an arithmetic sequence the terms never shrink towards zero, because the same constant is added each time. 3. Adding terms that do not shrink keeps pushing the total further out. 4. So the total heads off to positive or negative infinity and no limit exists. 5. Some geometric series do converge, because their terms can shrink towards zero. _Source: Siyavula Mathematics Grade 12 (Everything Maths, CC BY 4.0), Chapter 1: Sequences and series_

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