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Math Help - Arithmetic Sequences: Please Help :'(

  1. #1
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    Arithmetic Sequences: Please Help :'(

    (Arithmetic Sequences)

    How do I find K, given the consecutive arithmetic terms:
    1. k, 8, k+11
    2. k+2, 2k+3, 17

    The only example we were given is:
    -1 - (k+5) = (2k-1) - (-1)
    -1 - k - 5 = 2k - 1 +1
    -k -6 = 2k
    -6 = 3k
    k = -2

    ... which doesn't really apply, particularly through the first one.

    I managed to figure out one:
    31, k, 13
    31-13=18
    18/2=9
    31-9=22
    --> purely based on logic though, I don't know how to do the previous two.
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  2. #2
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    Hello, juliak!

    How do I find k, given the consecutive arithmetic terms:

    . . 1)\;\; k,\: 8,\: k+11\qquad\qquad 2)\;\;k+2,\:2k+3,\:17

    We are expected to know that with an arithmetic sequence,
    . . consecutive terms have a common difference, d.
    That is: . d \:=\:a_2-a_1,\;\;d \:=\:a_3-a_2


    In the first problem, we have: . a_1 \:=\:k,\;\;a_2\:=\:8,\;\;a_3 \:=\:k+11

    . . d \:=\:8 - k .[1]

    . . d \:=\:(k+11) - 8 \quad\Rightarrow\quad d \:=\:k+3 .[2]


    Equate [1] and [2]: . 8 - k \:=\:k + 3 \quad\Rightarrow\quad -2k \:=\:-5


    Therefore: . \boxed{k \:=\:\frac{5}{2}}


    Now try #2 yourself . . .

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