Math/Precal

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what is the first term of an arithmetic sequence if the 7th term is 21 and the 10th term is 126

  • Math/Precal -

    For an arithmetic sequence, the nth term is given by:
    T(n)=T(0)+kn,
    where k is a constant.

    Knowing T(7)=21, and T(10)=126
    we find k using
    T(10)-T(7) = 126-21
    T(0)+10k - (T(0)+7k) = 105
    3k = 105
    k=35
    From the value of k, we find T(0):
    T(n)=T(0)+35n
    T(7)=T(0)+35(7) = 21
    T(0)=21-245=-224

    T(n) = -224 + 35n

  • Math/Precal -

    7th term is 21 ----> a+6d = 21
    10th term is 126 ---> a + 9d = 126
    subtract them:
    3d = 105
    d = 35
    back in a+6d = 21 -----> a = -189

    first term is -189

    check:
    t7 = -189 + 6(35) = 21
    t10 = -189 + 9(35) = 126

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