the expression $n^{2}+n$ represents the total number of blocks used in the $n$th figure of a pattern. use…

the expression $n^{2}+n$ represents the total number of blocks used in the $n$th figure of a pattern. use the equation $n^{2}+n = 56$ to determine which figure has 56 blocks. figure 1 figure 2 figure 3 figure has 56 blocks.

the expression $n^{2}+n$ represents the total number of blocks used in the $n$th figure of a pattern. use the equation $n^{2}+n = 56$ to determine which figure has 56 blocks. figure 1 figure 2 figure 3 figure has 56 blocks.

Answer

Explanation:

Step1: Rearrange the equation

We have the quadratic equation $n^{2}+n - 56=0$.

Step2: Factor the quadratic

We factor $n^{2}+n - 56$ as $(n + 8)(n - 7)=0$.

Step3: Solve for n

Set each factor equal to zero: If $n+8 = 0$, then $n=-8$. If $n - 7=0$, then $n = 7$. Since $n$ represents the figure number and cannot be negative, we discard $n=-8$.

Answer:

7