advanced math

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suppose that a1, a2, a3, ..., ak forms an arithmetic sequence. If a5+a8+a11=10, a7+a10+a13=12, and ak=11, find k

note: the numbers and the k after the a's are subscript but i don't know how to type that

  • advanced math -

    from your first equation :
    a+4d + a+7d + a+10d = 10
    3a + 21d = 10 (#1)

    from your second equation :
    a+6d + a+9d + a+12d = 12
    3a 27d = 12 (#2)

    subtract #2 - #1
    6d = 2
    d = 1/3
    back in #1, 3a + 21(1/3) = 10
    a = 1

    then a+(kn-1)d = 11
    1 + (k-1)(1/3) = 11
    3 + k-1 = 33
    k = 31

    check : term(31) = a+30d
    = 1 + 30(1/3)
    = 1 + 10 = 11 Yea!!!

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