Question

9. how many sticks are needed for the 91st pattern10. write the linear equation for the squares and triangle in y=mx+b form

Answer 1

9) We can see that the sticks follow an aritmetic serie, where in each step he increase 7 sticks, and we know that the first pattern has 12 steacs so the 91 patern will have:

$\begin{gathered} a_{91}=12+(91-1)\cdot7 \\ a_{91}=12+90\cdot7 \\ a_{91}=642 \end{gathered}$

10) Now we can made a linear equation for the squares and the triangles, So first we will work with the squares, so we can see that they increas 1 by 1 so the slope will be equal to 1 and the intercept will be 0,0 so

$y=x$

So if we are in our first pattern x=1 and y =1, if we are in our second pattern x=2 and y=2 so this is true for the squares.

And for the triangle they are increasing 2 by 2 so the equation will be:

$y=2x+2$