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25 August, 20:55

Find the first term, a1, of an arithmetic sequence if a12 = 38 and a45 = 170.

-6

132/33

-5

6

+4
Answers (1)
  1. 25 August, 21:13
    0
    Standard formula for arithmetic sequence:

    an = a0 + d (n-1)

    if we use the two terms given, setting a12 as starting term and a45 as the end term an.

    170 = 38 + 33d

    170 - 38 = 33d

    132 = 33d

    132/33 = d

    This is the common difference, use it to find the first term.

    38 = a0 + (132/33) (12-1)

    38 = a0 + (132/33) (11)

    38 = a0 + 132/3

    38 - 132/3 = a0

    38 - 44 = a0

    -6 = a0

    The starting term is - 6
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