We have the following:
The first thing is to calculate the equation for the pattern, which would be the following
[tex]\begin{gathered} a_n=a_1+d\cdot(n-1) \\ a_1=4 \\ d=3 \\ \text{ replacing} \\ a_n=4+3\cdot(n-1) \end{gathered}[/tex]Therefore:
1. how many blocks would be in the 6th pattern
[tex]\begin{gathered} a_6=4+3(6-1) \\ a_6=19 \end{gathered}[/tex]2. how many blocks would be in the 77th pattern
[tex]\begin{gathered} a_{77}=4+3(77-1) \\ a_{77}=232 \end{gathered}[/tex]3. what pattern number would have 247 blocks
[tex]\begin{gathered} 247=4+3(n-1) \\ 3(n-1)=247-4 \\ n-1=\frac{243}{3} \\ n=81+1 \\ n=82 \end{gathered}[/tex]4. what is the linear equation for this pattern
[tex]\begin{gathered} y=4+3\cdot(x-1) \\ y-4=3(x-1) \\ or \\ y=3x+1 \end{gathered}[/tex]5. where do you see your slope in the pattern
[tex]\begin{gathered} y-y_1=m\cdot(x-x_1) \\ \text{ where m is the slope, therefore},\text{ in this case:} \\ m=3 \end{gathered}[/tex]6. where do you see your y-intercept in the pattern​
[tex]\begin{gathered} y=4+3x-3 \\ y=3x+1 \\ y=mx+b \\ \text{where b is the y-intercept, therefore} \\ b=1 \end{gathered}[/tex]