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6 May, 18:10

How many terms are in the arithmetic sequence 6, 2, - 2, ..., - 102?

Hint: an = a1 + d (n - 1), where a1 is the first term and d is the common difference

27

28

29

30

+5
Answers (1)
  1. 6 May, 18:36
    0
    The number of sequence in the arithmetic sequence given by:

    6, 2, - 2, ..., - 102

    will evaluated as follows:

    the explicit formula is:

    an=a1+d (n-1)

    a1=first term

    d=common difference

    n=number of terms

    thus from the question:

    a1=6

    d=2-6=-4

    an=-102

    plugging the values in the expression we get:

    -102=6-4 (n-1)

    solving for n we shall have:

    -102-6=-4 (n-1)

    -108=-4 (n-1)

    27=n-1

    thus

    n=27+1

    n=28

    Answer: 28 terms
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