Math - Arithmetic Sequences

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The sum of the 4th and the 14th term of an arithmetic sequence equals 22. The 9th term is 4 larger than the 4th term. Calculate the first term of the sequence.
I've been trying to solve this for like an hour but I just can't figure out how to do it! I'd really appreciate your help! Thanks!!

  • Math - Arithmetic Sequences -

    "The sum of the 4th and the 14th term of an arithmetic sequence equals 22" ----> a+3d + a+13d = 22
    2a + 16d = 22
    a + 8d = 11 (#1)

    "The 9th term is 4 larger than the 4th term" ---> a+8d - (a+3d) = 4
    5d = 4
    d = 4/5

    a = 11-8d
    a = 11 - 8(4/5) = 23/5

    check:
    t4 = 23/5 + 3(4/5) = 35/5 = 7
    t9 = 23/5 + 8(4/5) = 55/5 = 11
    t14 = 23/5 + 13(4/5) = 75/5 = 15

    11+15 = 22
    11-7=4

    all is good

  • Math - Arithmetic Sequences -

    The third term of an arithmetic sequence is 15, and the fifth term is 37. What is the first term?

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