Arithmetic Progressions Fill in the Blanks Quiz
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Questions and Answers

In the arithmetic progression (AP) 16, 11, 6..., with 23 terms, what is the common difference?

  • -3
  • 5
  • 3 (correct)
  • -5

    • If the sum of the first 14 terms of an AP is 1050 and the first term is 10, what is the value of the common difference?

  • 8
  • 14
  • 12
  • 10 (correct)

    • For the AP: -1, -0.5, -1.0, -1.5..., with 10 terms, what is the sum of the series?

  • -16
  • -18
  • -20 (correct)
  • -22

    • If an AP has a first term of 24 and a common difference of -3, what is the sum of the series if it has 8 terms?

    <p>-60</p> Signup and view all the answers

    How many terms of the AP 24, 21, 18... must be taken so that their sum is 78?

    <p>13</p> Signup and view all the answers

    What is the 20th term of an AP with a first term of 10 and a sum of the first 14 terms being 1050?

    <p>200</p> Signup and view all the answers

    What is the difference between a2 - a1 and a3 - a2?

    <p>0</p> Signup and view all the answers

    Which of the following lists of numbers forms an arithmetic progression?

    <p>The cost of digging a well, starting at <code>150 for the first metre and increasing by</code> 50 for each subsequent metre.</p> Signup and view all the answers

    What is the next term in the list 4x, 5x, 6x?

    <p>8x</p> Signup and view all the answers

    If ak+1 - ak is constant, what type of sequence is formed?

    <p>Arithmetic progression</p> Signup and view all the answers

    What is the sum of -5 and -2?

    <p>-7</p> Signup and view all the answers

    What mathematical concept relates to a4 - a3 = 1?

    <p>Subtraction</p> Signup and view all the answers

    What is the second term of the geometric progression when the first term is 3 and the common ratio is 2?

    <p>6</p> Signup and view all the answers

    In a geometric progression, what is the third term if the second term is 6 and the common ratio is 2?

    <p>24</p> Signup and view all the answers

    What is the 30th term of the arithmetic progression 10, 7, 4,...?

    <p>-77</p> Signup and view all the answers

    What are the terms in the geometric progression with a first term of 256 and a common ratio of -1/2?

    <p>-128, 64, -32, ...</p> Signup and view all the answers

    Which term of the arithmetic progression -3, -1, 2,... is the 11th term?

    <p>9</p> Signup and view all the answers

    What is the common ratio of the geometric progression with terms 25, -5, 1, -1?

    <p>-1/5</p> Signup and view all the answers

    In the arithmetic progression with a1 = 2 and a3 = 26, what is the value of a2?

    <p>10</p> Signup and view all the answers

    Which of the following lists of numbers form a geometric progression?

    <p>(i) 3, 6, 12, ...</p> Signup and view all the answers

    For the arithmetic progression a1 = -4 and a6 = 6, what are the values of a2, a3, a4, and a5?

    <p>-2, 0, 2, 4</p> Signup and view all the answers

    How can you determine if a list of numbers forms a geometric progression?

    <p>By multiplying each number by a constant value</p> Signup and view all the answers

    Which term of the arithmetic progression 3, 8, 13,... is equal to 78?

    <p>23</p> Signup and view all the answers

    If the 3rd and 9th terms of an arithmetic progression are 4 and -8 respectively, which term of this AP is zero?

    <p>6th term</p> Signup and view all the answers

    Why is it important for students to reflect and express their new formulations?

    <p>To relate abstract ideas to their own experiences</p> Signup and view all the answers

    What does the text emphasize regarding language and Mathematics?

    <p>The need to keep language simple</p> Signup and view all the answers

    Why is it suggested to allow children to reflect and use language?

    <p>To provide an opportunity for reflection and expression</p> Signup and view all the answers

    What is the main purpose of the book according to the text?

    <p>To help teachers and students connect abstract ideas with real-life experiences</p> Signup and view all the answers

    What does the text hope teachers and assessment task formulators will recognize?

    <p>The importance of students' reflections and language use</p> Signup and view all the answers

    What does the author salute at the end of the text?

    <p>The effort of the authors in working together as a team</p> Signup and view all the answers

    Study Notes

    Relating Mathematics to Real-Life Experiences

    • Importance of relating abstract mathematical concepts to real-life experiences for students to better understand and organize their experiences
    • Need for students to have opportunities to reflect and express their thoughts, using language and mathematical formulations to describe events around them

    Classroom Emphasis

    • Emphasis on the importance of language and Mathematics interplay in the classroom
    • Need for teachers to provide opportunities for students to reflect and use language to describe their experiences

    Arithmetic Progressions (AP)

    • Definition of AP: a sequence of numbers where each term is obtained by adding a fixed constant to the previous term
    • Examples of AP: 5, 7, 9, 11, ... (where each term is obtained by adding 2 to the previous term)
    • Formula for nth term of an AP: an = a1 + (n-1)d, where a1 is the first term and d is the common difference

    Exercises and Examples

    • Exercises to identify whether a list of numbers forms an AP
    • Examples of APs: 10, 7, 4, 1, ...; -3, -2, -1, 0, ...
    • Formula for finding the nth term of an AP: an = a1 + (n-1)d
    • Examples of finding the nth term of an AP: 30th term of the AP 10, 7, 4, ...; 11th term of the AP -3, -2, -1, 0, ...

    Applications of AP

    • Real-life applications of AP: calculating the cost of digging a well, the amount of money in a savings account, etc.
    • Examples of APs in real-life scenarios: the cost of digging a well, the amount of money in a savings account, etc.

    Geometric Progressions (GP)

    • Definition of GP: a sequence of numbers where each term is obtained by multiplying the previous term by a fixed constant
    • Examples of GP: 2, 6, 18, 54, ... (where each term is obtained by multiplying the previous term by 3)
    • Formula for nth term of a GP: an = ar^(n-1), where a is the first term and r is the common ratio

    Exercises and Examples

    • Exercises to identify whether a list of numbers forms a GP
    • Examples of GPs: 3, 6, 12, 24, ...; 256, -128, 64, -32, ...
    • Formula for finding the nth term of a GP: an = ar^(n-1)
    • Examples of finding the nth term of a GP: the GP with a = 3 and r = 2, the GP with a = 256 and r = -1/2

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    Description

    Test your knowledge on Arithmetic Progressions by filling in the blanks in the provided table and finding the nth terms for different AP series. Solve for specific terms in given AP sequences. Perfect for practicing AP concepts and formulae.

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