Write an Equation using the following arithmetic sequence: 5, _____, ______, 32

Question

Write an Equation using the following arithmetic sequence: 5, _____, ______, 32

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Vân Khánh 2 weeks 2021-08-29T19:33:02+00:00 1 Answers 0 views 0

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    2021-08-29T19:34:18+00:00

    Answer:

    The sequence is:

    5, 14, 23, 32

    Step-by-step explanation:

    We know that an Arithmetic sequence with a₁ and the commo difference ‘d’ has the nth term such as:

    aₙ = a₁ + (n-1)d

    Given the arithmetic sequence

    5, _____, ______, 32

    here:

    a₁ = 5

    n = 4

    aₙ

    so substituting a₁ = 5, n = 4 and aₙ = 32 in the nth term

    aₙ = a₁ + (n-1)d

    32 = 5 + (4-1)d

    32 = 5 + 3d

    3d = 32-5

    3d = 27

    divide both sides by 3

    3d/3 = 27/3

    d = 9

    Therefore, the common difference: d = 9

    Determining the 2nd term:

    Using the formula

    aₙ = a₁ + (n-1)d

    substitute n = 2, a₁ = 5, d = 9

    a₂ = 5 + (2-1)9

    a₂ = 5 + 1(9)

    a₂ = 5 + 9

    a₂ = 14

    Determining the 3rd term:

    Using the formula

    aₙ = a₁ + (n-1)d

    substitute n = 3, a₁ = 5, d = 9

    a₃ = 5 + (3-1)9

    a₃ = 5 + 2(9)

    a₃ = 5 + 18

    a₃ = 23

    Thus, the sequence becomes:

    5, 14, 23, 32

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