Suzi builds L shapes with blocks. An L shape that is 3 blocks high uses 7 blocks. We need to find how many blocks are needed to build an L shape that is 100 blocks high.

1. Problem Description

Suzi builds L shapes with blocks. An L shape that is 3 blocks high uses 7 blocks. We need to find how many blocks are needed to build an L shape that is 100 blocks high.

2. Solution Steps

Let $n$ be the height of the L shape. We want to find a formula for the number of blocks needed to build an L shape of height $n$.

When $n=1$, the number of blocks is

1. When $n=2$, the number of blocks is

4. When $n=3$, the number of blocks is

7.

Let $b(n)$ be the number of blocks needed for an L-shape of height $n$.

$b(1) = 1$

$b(2) = 4$

$b(3) = 7$

We observe that the difference between consecutive terms is constant, i.e., $b(2) - b(1) = 4 - 1 = 3$ and $b(3) - b(2) = 7 - 4 = 3$.

Therefore, we can assume that $b(n)$ is a linear function of $n$ in the form $b(n) = an + c$ for some constants $a$ and $c$.

Using $b(1) = 1$ and $b(2) = 4$, we have:

$a(1) + c = 1$

$a(2) + c = 4$

Subtracting the first equation from the second equation, we get:

$a = 3$

Substituting $a=3$ into the first equation, we have:

$3(1) + c = 1$

$c = 1 - 3 = -2$

So, $b(n) = 3n - 2$.

Now, let's check if this formula works for $n=3$:

$b(3) = 3(3) - 2 = 9 - 2 = 7$. This matches the given information.

Now we can find the number of blocks needed for an L-shape that is 100 blocks high:

$b(100) = 3(100) - 2 = 300 - 2 = 298$

3. Final Answer

298