Arithmetic and Geometric Series Formulas Quiz
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Questions and Answers

In a geometric series, if the 1st term is 2 and the common ratio is 3, what is the 4th term?

  • 54
  • 27 (correct)
  • 81
  • 18
  • For an arithmetic sequence, if the 5th term is 32 and the 9th term is 56, what is the common difference?

  • 7 (correct)
  • 6
  • 5
  • 8
  • Find the sum of the first 7 terms of the arithmetic series where the 1st term is 3 and the common difference is 4.

  • 85
  • 101 (correct)
  • 92
  • 98
  • Identify the type of sequence: 3, 6, 12, 24, ...

    <p>Geometric sequence</p> Signup and view all the answers

    If the 11th term of an arithmetic sequence is 45 and the common difference is 4, what is the 21st term?

    <p>89</p> Signup and view all the answers

    For a geometric series with a 1st term of 5 and a common ratio of 2, find the sum of the first 6 terms.

    <p>955</p> Signup and view all the answers

    What is the defining characteristic of an arithmetic sequence?

    <p>Each term is created by adding or subtracting a definite number to the preceding number</p> Signup and view all the answers

    In a geometric sequence, how is each term obtained?

    <p>By multiplying or dividing a definite number with the preceding number</p> Signup and view all the answers

    What is the formula to find the nth term in an arithmetic sequence?

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

    For a geometric sequence, what happens if the common ratio is greater than 1?

    <p>The terms increase at an increasing rate</p> Signup and view all the answers

    What does the sum of all terms in a sequence form?

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

    What is the formula to compute the 21st term of an arithmetic sequence?

    <p>an = a1 + (n - 1)d</p> Signup and view all the answers

    In an arithmetic sequence, if the common difference is 3 and the first term is 4, what is the 21st term?

    <p>61</p> Signup and view all the answers

    Which term is referred to as the common ratio in a geometric series?

    <p>First term</p> Signup and view all the answers

    What does the formula Sn = n(a1 + an)/2 represent in a series computation?

    <p>Sum of all terms</p> Signup and view all the answers

    In a geometric series, what does it mean if the common ratio between terms is 0.5?

    <p>Each term is halved</p> Signup and view all the answers

    Study Notes

    Sequences and Series

    • A sequence is an arrangement of objects or numbers in a particular order, following a specific rule.
    • A sequence can be finite or infinite, depending on the number of terms.
    • If 𝑎1, 𝑎2, 𝑎3, 𝑎4 … denotes the terms of the sequence, then 1, 2, 3, 4… denotes the position of the term.

    Types of Sequences

    • Arithmetic Sequence: every term is created by adding or subtracting a definite number to the preceding number.
    • Geometric Sequence: every term is obtained by multiplying or dividing a definite number with the preceding number.
    • Harmonic Sequence: if the reciprocals of all the elements of a sequence form an arithmetic sequence.
    • Fibonacci Numbers: each element is obtained by adding two preceding elements, starting with 0 and 1.

    Formulas

    • Arithmetic Sequence: 𝑎𝑛 = 𝑎1 + (𝑛 − 1)𝑑
    • Geometric Series: 𝑎𝑛 = 𝑎1 𝑟^(𝑛−1), 𝑆𝑛 = 𝑎1 (1 − 𝑟^n) / (1 − 𝑟)
    • Harmonic Sequence: reciprocal of each term forms an arithmetic progression

    Examples

    • In an arithmetic sequence, the common difference is obtained by subtracting the first term from the second term.
    • In a geometric series, the common ratio is obtained by dividing any two consecutive terms.
    • In a harmonic sequence, the reciprocal of each term forms an arithmetic progression.

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    Description

    Test your knowledge of arithmetic and geometric series formulas with examples provided. Learn how to calculate the 21st term and sum of terms in a series using the given formulas.

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