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Math Help - Find the arithmetic progression

  1. #1
    Junior Member
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    Find the arithmetic progression

    1. Find the arithmetic progression where t5 = 17 and t12 = 52

    2. Find t6 of an arithmetic sequence given that t3 = 5.6 and t12 = 7

    3. Find the 7th term of the arithmetic progression whose 5th term is m and whose 11th term is n.

    4. Find the value of p so that p + 5, 4p + 3, 8p -2 will form successive terms of an arithmetic progression
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  2. #2
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    Hello, nerdzor!

    This should get you started . . .


    1. Find the arithmetic progression where: t_5 = 17\text{ and }t_{12} = 52
    \text{The }n^{th}\text{ term is: }\;t_n \;=\;t_1 + (n-d)d
    . . \text{where }t_1\text{ is the first term and }d\text{ is the common difference.}


    We have: . \begin{array}{cccccc}t_5 & = & t_1 + 4d &^ = & 17 & [1] \\ t_{12} &=& t_1 + 11d & = & 52 & [2] \end{array}

    Subtract [1] from [2]: . 7d \:=\:35\quad\Rightarrow\quad\boxed{ d \:=\:5}

    Substitute into [1]: . t_1 + 4(5) \:=\:17\quad\Rightarrow\quad\boxed{ t_1 \:=\:-3}


    The progression is: . -3,\:2,\:7,\:12,\:17,\:22,\:27,\:32.\:37.\:42.\:47,  \;52,\:\cdots




    4. Find the value of p so that: p + 5,\;4p + 3,\;8p -2
    are successive terms of an arithmetic progression.
    Consecutive terms will have a common difference.

    Hence: . (4p+3) - (p + 5) \;=\;(8p-2) - (4p+3)

    . . And solve for p\!:\;\;\boxed{p \:=\:3}

    [The terms are: . 8,\:15,\text{ and }22.]

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