Arithmetic Progressions Quiz
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Questions and Answers

Which of the following is the correct equation to find the nth term of an arithmetic progression?

  • $a_n = a_1 + (n + 1)d$
  • $a_n = a_1 \cdot (n - 1)d$
  • $a_n = a_1 \cdot (n + 1)d$
  • $a_n = a_1 + (n - 1)d$ (correct)

    • Which term of the arithmetic progression 2, 5, 8, 11, ... is 23?

  • $a_7$
  • $a_9$
  • $a_8$ (correct)
  • $a_6$

    • What is the common difference of the arithmetic progression 10, 7, 4, 1, ...?

  • $-3$ (correct)
  • $-1$
  • $-2$
  • $3$

    • What is the sum of the arithmetic series 3, 6, 9, 12, ..., 99?

    <p>$1485$</p> Signup and view all the answers

    According to the anecdote, who reinvented the method to compute arithmetic progressions?

    <p>Carl Friedrich Gauss</p> Signup and view all the answers

    Study Notes

    Arithmetic Progression (AP) Basics

    • The nth term of an Arithmetic Progression can be calculated using the formula:
      • nth term = a + (n - 1)d
      • where 'a' is the first term, 'd' is the common difference, and 'n' is the term number.

    Finding Specific Terms

    • In the AP 2, 5, 8, 11, ..., to find which term equals 23:
      • Use the nth term formula: 23 = 2 + (n - 1)3.
      • Solving gives n = 8, meaning 23 is the 8th term.

    Common Difference

    • For the AP 10, 7, 4, 1, ..., the common difference 'd' can be identified:
      • d = second term - first term = 7 - 10 = -3.
      • This indicates a decreasing sequence.

    Sum of the Series

    • The sum of the arithmetic series 3, 6, 9, 12, ..., 99 can be calculated:
      • First find the number of terms (n):
        • Last term (99) = first term (3) + (n - 1) * common difference (3).
        • Solve for n, yielding n = 33.
      • Then use the formula for the sum:
        • Sum = n/2 * (first term + last term), resulting in a total sum of 1683.

    Historical Note

    • The anecdote attributes the reinvention of methods to compute arithmetic progressions to prominent mathematicians, although the specific names may vary based on context.

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    Description

    Test your knowledge of arithmetic progressions with this quiz! Learn about the common difference and identify arithmetic progressions from given sequences.

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