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21 December, 08:58

If aₙ = 3 (3) ⁿ⁻1, what is S₃?

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Answers (2)
  1. 21 December, 11:11
    0
    S3 = 39

    Step-by-step explanation:

    * an = 3 (3) ^ (n-1) is a geometric sequence

    * The general rule of the geometric sequence is:

    an = a (r) ^ (n-1)

    Where:

    a is the first term

    r is the common difference between each consecutive terms

    n is the position of the term in the sequence

    The rules means:

    - a1 = a, a2 = ar, a3 = ar², a4 = ar³, ...

    ∵ an = 3 (3) ^ (n-1)

    ∴ a = 3 and r = 3

    ∴ a1 = 3

    ∴ a2 = 3 (3) = 9

    ∴ a3 = 3 (3) ² = 27

    * S3 = a1 + a2 + a3

    ∴ S3 = 3 + 9 + 27 = 39

    Note:

    We can use the rule of the sum:

    Sn = a (1 - r^n) / (1 - r)

    S3 = 3 (1 - 3³) / 1 - 3 = 3 (1 - 27) / -2 = 3 (-26) / -2 = 3 (13) = 39
  2. 21 December, 11:43
    0
    The correct answer is S₃ = 39

    Step-by-step explanation:

    It is given that,

    aₙ = 3 (3) ⁿ⁻¹

    To find a₁

    a₁ = 3 (3) ¹⁻¹ = 3 (3) °

    = 3 * 1 = 3

    To find a₂

    a₂ = 3 (3) ²⁻¹ = 3 (3) ¹

    = 3 * 3 = 9

    To find a₃

    a₃ = 3 (3) ³⁻¹ = 3 (3) ²

    = 3 * 9 = 27

    To find the value of S₃

    S₃ = a₁ + a₂ + a₃

    = 3 + 9 + 27 = 39

    Therefore the correct answer is S₃ = 39
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