Arithmetic Progression
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Questions and Answers

What is the common difference in the arithmetic progression 2, 5, 8, 11,...?

  • 1
  • 3 (correct)
  • 4
  • 2

    • What is the formula to calculate the nth term in an arithmetic progression?

  • an = a * (n - 1)d
  • an = a - (n - 1)d
  • an = a + (n - 1)d (correct)
  • an = a / (n - 1)d

    • What is the sequence of numbers 10, 15, 20, 25,... an example of?

  • Quadratic progression
  • Geometric progression
  • Harmonic progression
  • Arithmetic progression (correct)

    • What is the sum of the first n terms in an arithmetic progression calculated using?

    <p>Sn = (n/2)(2a + (n - 1)d)</p> Signup and view all the answers

    Which of the following is an application of arithmetic progressions?

    <p>Modeling real-world problems involving uniform change</p> Signup and view all the answers

    What is a key feature of an arithmetic progression?

    <p>The sequence increases or decreases by a fixed amount at each step</p> Signup and view all the answers

    What is the value of the 10th term in an arithmetic progression with a first term of 5 and a common difference of 3?

    <p>29</p> Signup and view all the answers

    What is the sum of the first 10 terms of an arithmetic progression with a first term of 2 and a last term of 20?

    <p>110</p> Signup and view all the answers

    What is the value of the 7th term in an arithmetic progression with a first term of 10 and a common difference of -2?

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

    If the 5th term of an arithmetic progression is 17 and the common difference is 3, what is the first term?

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

    What is the sum of the first 5 terms of an arithmetic progression with a first term of 3 and a last term of 15?

    <p>40</p> Signup and view all the answers

    If the 3rd term of an arithmetic progression is 12 and the 5th term is 18, what is the common difference?

    <p>3</p> Signup and view all the answers

    Study Notes

    Definition

    An arithmetic progression (AP) is a sequence of numbers in which each term after the first is obtained by adding a fixed constant to the previous term.

    Key Features

    • Common difference (d): the fixed constant added to each term to get the next term
    • First term (a): the starting point of the sequence
    • Formula: an = a + (n - 1)d, where an is the nth term

    Examples

    • 2, 5, 8, 11, ... (d = 3, a = 2)
    • 10, 15, 20, 25, ... (d = 5, a = 10)

    Properties

    • The sequence increases or decreases by a fixed amount (d) at each step
    • The nth term can be calculated using the formula an = a + (n - 1)d
    • The sum of the first n terms (Sn) can be calculated using the formula Sn = (n/2)(2a + (n - 1)d)

    Applications

    • Modeling real-world problems involving uniform change, such as population growth, financial transactions, and motion
    • Solving problems involving sequences and series
    • Used in various fields, including mathematics, physics, engineering, and economics

    Arithmetic Progression (AP)

    • A sequence of numbers where each term after the first is obtained by adding a fixed constant (common difference) to the previous term

    Key Features of AP

    • Common difference (d): the fixed constant added to each term to get the next term
    • First term (a): the starting point of the sequence
    • Formula: an = a + (n - 1)d, where an is the nth term

    Examples of AP

    • 2, 5, 8, 11,... (d = 3, a = 2)
    • 10, 15, 20, 25,... (d = 5, a = 10)

    Properties of AP

    • The sequence increases or decreases by a fixed amount (d) at each step
    • The nth term can be calculated using the formula an = a + (n - 1)d
    • The sum of the first n terms (Sn) can be calculated using the formula Sn = (n/2)(2a + (n - 1)d)

    Applications of AP

    • Used to model real-world problems involving uniform change, such as:
      • Population growth
      • Financial transactions
      • Motion
    • Used to solve problems involving sequences and series
    • Applications in various fields, including:
      • Mathematics
      • Physics
      • Engineering
      • Economics

    Arithmetic Progression

    Formula

    • An arithmetic progression is a sequence of numbers where each term is obtained by adding a fixed constant to the previous term.
    • The formula to find the nth term is: an = a1 + (n - 1) * d
    • In this formula: an is the nth term, a1 is the first term, n is the term number, and d is the common difference.

    Sum

    • The formula to find the sum of the first n terms is: Sn = (n/2) * (a1 + an)
    • In this formula: Sn is the sum of the first n terms, a1 is the first term, and an is the nth term.

    Nth Term

    • The nth term can be found using the formula: an = a1 + (n - 1) * d
    • Alternatively, the nth term can be found using the formula: an = a(n-1) + d
    • In both formulas: an is the nth term, a1 is the first term, n is the term number, and d is the common difference.

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    Quiz Team

    Description

    Learn about arithmetic progressions, their key features, and formulas. Understand how to identify and work with sequences of numbers where each term is obtained by adding a fixed constant.

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