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Math Help - Sequence Problem

  1. #1
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    Exclamation Sequence Problem

    Please Help :

    If The t3=8 And t8=23 In An Arithmetic Sequence, Find a (Intital Term) And d (Common Difference) .

    Thanks In Advance .
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  2. #2
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    The third term is 8, the 8th term is 23. So, in the space of 5 terms, we covered a "distance" of 15. Thus, the common difference is 15/5 or 3.

    To find the first term, let's work backwards from the third term. Since we're working backwards, instead of adding 3, we'll subtract 3.

    Second term = 8 - 3 = 5.

    Third term = 5 - 3 = 2.
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  3. #3
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    Hello, JennV!

    If t_3=8\text{ and }t_8=23 in an arithmetic sequence,
    find a (first term) and d (common difference).
    We're expected to be familiar with the formula: . t_n \:=\:a + (n-1)d

    . . \begin{array}{cccc}t_3\:=\:8 & \Rightarrow & a + 2d \:=\:8 & {\color{blue}[1]}\\ t_8 \:=\:23 & \Rightarrow & a + 7d \:=\:23 & {\color{blue}[2]}\end{array}

    Subtract [1] from [2]: . 5d \:=\:15 \quad\Rightarrow\quad \boxed{d \:=\:3}

    Substitute into [1]: . a + 2(3)\:=\:8 \quad\Rightarrow\quad \boxed{a \:=\:2}

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