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 $\displaystyle t_1=3$

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 $\displaystyle t_1=3$
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?

3. Originally Posted by danny arrigo
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?
yes thank you sir. what does the \cdot mean in your second suggestion?

4. Originally Posted by danny arrigo
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?
is it $\displaystyle t_n=t_{n-1}+3$ for $\displaystyle t_1=3?$

5. Originally Posted by william
is it $\displaystyle t_n=t_{n-1}+3$ for $\displaystyle t_1=3?$
Oh so close

$\displaystyle t_n = t_{n-1}+ 3n$

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

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