# Thread: recursive formula

1. ## 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 $t_1=3$

2. Originally Posted by william
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

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

or

$\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?

3. Originally Posted by danny arrigo
Notice the pattern

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

or

$\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?
yes thank you sir. what does the \cdot mean in your second suggestion?

4. Originally Posted by danny arrigo
Notice the pattern

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

or

$\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?
is it $t_n=t_{n-1}+3$ for $t_1=3?$

5. Originally Posted by william
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.