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Math Help - Arithmetic Sequence help!

  1. #1
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    Arithmetic Sequence help!

    So I was going over some of my Algebra II work and the part that we're going over is COMPLETELY different than the practice problems. We have this question that I didn't even see the directions for how to solve like this:

    What are the missing terms of the arithmetic sequence -8, ___, ___, 3

    I know that the difference is 11 between the two numbers, but I've tried every way possible to get the correct answer. I don't understand how to do it at all. Help, please?
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  2. #2
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    Quote Originally Posted by delovely9109 View Post
    So I was going over some of my Algebra II work and the part that we're going over is COMPLETELY different than the practice problems. We have this question that I didn't even see the directions for how to solve like this:

    What are the missing terms of the arithmetic sequence -8, ___, ___, 3

    I know that the difference is 11 between the two numbers, but I've tried every way possible to get the correct answer. I don't understand how to do it at all. Help, please?
    U_{n} = a + (n-1)d

    where U_n is the value of term n, a is the first term, n is the number of terms and d is the common difference.

    In your case we have a = -8 and U_4 = 3

    Putting what is known into the formula:

    3 = -8 + (4-1)d and it's not hard to see that d = \frac{11}{3}

    Therefore your missing numbers are -8 + \frac{11}{3} = -\frac{13}{3} and -8+2\frac{11}{3} = -\frac{2}{3}
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  3. #3
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    Hello, delovely9109!

    Another approach . . .


    What are the missing terms of the arithmetic sequence: -8, ___, ___, 3
    I must assume that you know something about Arithmetic Sequences.


    We have an arithmetic sequence with common difference d.

    . . \begin{array}{cc}\text{The first term is}&\text{-}8 \\ \text{The second term is:}&\text{-}8+d \\ \text{The third term is:}&\text{-}8+2d \\ \text{The fourth term is:}&\text{-}8+3d \end{array}

    But we already know that the fourth term is 3.

    So we have: . \text{-}8+3d \:=\:3\quad\Rightarrow\quad 3d \:=\:11\quad\Rightarrow\quad d \:=\:\tfrac{11}{3}


    Therefore, the sequence is: . \text{-}8,\;\text{-}\tfrac{13}{3},\;\text{-}\tfrac{2}{3},\;3,\;\hdots

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