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17 May, 06:36

For some number, t, the first 3 terms of an

arithmetic sequence are

t + 2, 3t, 4t + 1

Which of the following is the numerical value of the 4th

term.

+4
Answers (1)
  1. 17 May, 06:54
    0
    a₄ = 17

    Step-by-step explanation:

    The difference d between consecutive terms of an arithmetic sequence are constant, that is

    a₂ - a₁ = a₃ - a₂, substituting values

    3t - t - 2 = 4t + 1 - 3t

    2t - 2 = t + 1 (subtract t from both sides)

    t - 2 = 1 (add 2 to both sides)

    t = 3

    Thus

    a₁ = t + 2 = 3 + 2 = 5

    a₂ = 3t = 3 (3) = 9

    a₃ = 4t + 1 = 4 (3) + 1 = 12 + 1 = 13

    The first 3 terms of the sequence are

    5, 9, 13 with

    d = 9 - 5 = 13 - 9 = 4, thus

    a₄ = 13 + 4 = 17
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