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Math Help - recursive formula

  1. #1
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    recursive formula

    date: total toothpicks

    1 toothpicks:3
    2 toothpicks:9
    3 toothpicks:18
    4 toothpicks:30
    5 toothpicks:45
    6 toothpicks:63

    I) model the toothpick column with a recursive relationship with t_1=3
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  2. #2
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    Quote Originally Posted by william View Post
    date: total toothpicks

    1 toothpicks:3
    2 toothpicks:9
    3 toothpicks:18
    4 toothpicks:30
    5 toothpicks:45
    6 toothpicks:63

    I) model the toothpick column with a recursive relationship with t_1=3
    Notice the pattern

    \begin{array}{r}<br />
3 + 6 = 9\;\,\\<br />
9 + 9 = 18\\<br />
18 + 12 = 30 \\<br />
30 + 15 = 45\\<br />
45 + 18= 63\\<br />
\end{array}

    or

    \begin{array}{r}<br />
3 + 2 \cdot3 = 9\;\,\\<br />
9 + 3 \cdot3 = 18\\<br />
18 + 4 \cdot3 = 30 \\<br />
30 + 5 \cdot3 = 45\\<br />
45 + 6 \cdot3 = 63\\<br />
\end{array}<br />


    This help?
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  3. #3
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    Quote Originally Posted by danny arrigo View Post
    Notice the pattern

    \begin{array}{r}<br />
3 + 6 = 9\;\,\\<br />
9 + 9 = 18\\<br />
18 + 12 = 30 \\<br />
30 + 15 = 45\\<br />
45 + 18= 63\\<br />
\end{array}

    or

    \begin{array}{r}<br />
3 + 2 \cdot3 = 9\;\,\\<br />
9 + 3 \cdot3 = 18\\<br />
18 + 4 \cdot3 = 30 \\<br />
30 + 5 \cdot3 = 45\\<br />
45 + 6 \cdot3 = 63\\<br />
\end{array}<br />


    This help?
    yes thank you sir. what does the \cdot mean in your second suggestion?
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  4. #4
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    Quote Originally Posted by danny arrigo View Post
    Notice the pattern

    \begin{array}{r}<br />
3 + 6 = 9\;\,\\<br />
9 + 9 = 18\\<br />
18 + 12 = 30 \\<br />
30 + 15 = 45\\<br />
45 + 18= 63\\<br />
\end{array}

    or

    \begin{array}{r}<br />
3 + 2 \cdot3 = 9\;\,\\<br />
9 + 3 \cdot3 = 18\\<br />
18 + 4 \cdot3 = 30 \\<br />
30 + 5 \cdot3 = 45\\<br />
45 + 6 \cdot3 = 63\\<br />
\end{array}<br />


    This help?
    is it t_n=t_{n-1}+3 for t_1=3?
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  5. #5
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    Quote Originally Posted by william View Post
    is it t_n=t_{n-1}+3 for t_1=3?
    Oh so close

    t_n = t_{n-1}+ 3n

    PS the \cdot gives me a single cetered dot. It gives

    3 \cdot 2 insted of  3.2 sometimes confusing with decimals.
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