Multiple Choice Question (MCQ)

a, 2a − 1, 3a − 2, 4a − 3, . . .

For a particular number a, the first term in the sequence above is equal to a, and each term thereafter is 7 greater than the previous term. What is the value of the 16th term in the sequence

  1. ×

    75

  2. ×

    90

  3. ×

    110

  4. 113

Collected in the board: Arithmetic sequence

Steven Zheng posted 7 hours ago

Answer

  1. Since the second term is 7 greater than the first term, we have the following equation

    (2a − 1) − a = 7

    so that a = 8.

    The sequence is 8, 15, 22, . . . You can either continue to write out the sequence until the 16th term, or realize in a mathematical way.

    Observe the sequence a, 2a − 1, 3a − 2, 4a − 3, . . .. The general term of the sequence can be represented by the following expression

    a_n=na-(n-1)

    then the 16th term is

    16a − 15 = 16(8) − 15 = 128 − 15 = 113

    Therefore, D is correct

Steven Zheng posted 7 hours ago

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