Multiple Choice Question (MCQ)

The formula a_n = a_1 + (n - 1)d can be used to give a formula for the general term of the arithmetic sequence. For example, the sequence 3, 15, 27, 39, 51,\dots has a_1 = 3 and common difference d = 12, hence a formula for the general term is given by a_n = 3 + (n - 1)\cdotp 12 which simplifies: a_n = 12n - 9. Now your turn: Which of the following is the general term b_n of the sequence 20, 18, 16, 14, 12, \dots?

  1. ×

    b_n = 20 - 2n

  2. ×

    b_n = 18n

  3. b_n = 22 - 2n

  4. ×

    b_n = 18 - 2n

Collected in the board: Arithmetic sequence

Steven Zheng posted 2 months ago


Answer

  1. The common difference of the sequence 20, 18, 16, 14, 12, \dots is -2 and a_1=20.

    Plug in the formula for the general terms of an arithmetic sequence, so we get,

    a_n = a_1 + (n - 1)d=20+(n-1)(-2)=22-2n

Steven Zheng posted 2 months ago

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