Arithmetic Progressions Quiz
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Questions and Answers

What is an arithmetic progression?

  • A sequence of numbers with a variable difference between each pair of successive terms
  • A sequence of numbers with a constant difference between each pair of successive terms (correct)
  • A sequence of numbers with a variable ratio between each pair of successive terms
  • A sequence of numbers with a constant ratio between each pair of successive terms

    • What is the formula for the n-th term of an arithmetic progression?

  • $a_{n} = a_{1} + nd$
  • $a_{n} = a_{1} + (n - 1)d$ (correct)
  • $a_{n} = a_{1} - nd$
  • $a_{n} = a_{1} - (n - 1)d$

    • What is the common difference in the sequence 3, 6, 9, 12, 15?

  • 4
  • 3 (correct)
  • 5
  • 2

    • What is a finite portion of an arithmetic progression called?

    <p>Finite arithmetic progression</p> Signup and view all the answers

    What is the sum of a finite arithmetic progression called?

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

    What is the formula for the n-th term of an arithmetic progression?

    <p>$a_n = a_1 + (n - 1)d$</p> Signup and view all the answers

    What is the common difference in the sequence 4, 9, 14, 19, 24?

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

    What is a finite portion of an arithmetic progression called?

    <p>Finite arithmetic progression</p> Signup and view all the answers

    What is the sum of the first 10 terms of the arithmetic progression 2, 5, 8, 11, 14, ...?

    <p>120</p> Signup and view all the answers

    If the 7th term of an arithmetic progression is 29 and the common difference is 3, what is the first term of the progression?

    <p>14</p> Signup and view all the answers

    Study Notes

    Arithmetic Progression (AP)

    • An arithmetic progression is a sequence of numbers in which the difference between consecutive terms is constant. This difference is known as the common difference.

    n-th Term Formula

    • The formula for the n-th term of an arithmetic progression is given by:
      • ( a_n = a + (n - 1) d )
      • Where ( a ) is the first term, ( d ) is the common difference, and ( n ) is the term number.

    Common Difference

    • The common difference in the sequence 3, 6, 9, 12, 15 is 3, since each term increases by 3.
    • In the sequence 4, 9, 14, 19, 24, the common difference is 5, as each term increases by 5.

    Finite Portions

    • A finite portion of an arithmetic progression is referred to as a finite arithmetic sequence or segment.

    Sum of Finite Arithmetic Progression

    • The sum of a finite arithmetic progression is called the arithmetic series.

    Sum of the First 10 Terms

    • To find the sum of the first 10 terms of the arithmetic progression 2, 5, 8, 11, 14:
      • Use the sum formula: ( S_n = \frac{n}{2} (a + l) ),
      • Here ( n = 10 ), ( a = 2 ), and ( l = 14 ), yielding a sum of 80.

    Finding the First Term

    • If the 7th term of an arithmetic progression is 29 and the common difference is 3:
      • The 7th term can be expressed using the n-th term formula: ( 29 = a + (7 - 1) \cdot 3 )
      • Thus, the first term ( a ) is calculated to be 17.

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    Description

    Test your knowledge of arithmetic progressions with this quiz. Explore sequences of numbers with a constant difference between each term, and identify the common difference in various AP examples.

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