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 $\displaystyle t_1=3$

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- Jan 27th 2009, 11:02 AMwilliamrecursive 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 $\displaystyle t_1=3$ - Jan 27th 2009, 11:23 AMJester
Notice the pattern

$\displaystyle \begin{array}{r}

3 + 6 = 9\;\,\\

9 + 9 = 18\\

18 + 12 = 30 \\

30 + 15 = 45\\

45 + 18= 63\\

\end{array}$

or

$\displaystyle \begin{array}{r}

3 + 2 \cdot3 = 9\;\,\\

9 + 3 \cdot3 = 18\\

18 + 4 \cdot3 = 30 \\

30 + 5 \cdot3 = 45\\

45 + 6 \cdot3 = 63\\

\end{array}

$

This help? - Jan 27th 2009, 11:26 AMwilliam
- Jan 27th 2009, 11:44 AMwilliam
- Jan 27th 2009, 01:13 PMJester