What are 2D shapes and sequences? Provide definitions, examples, and applications.

The given terms are $2^2, 3^2, 4^2, 5^2$. This is a sequence of perfect squares where the $n$-th term is $T_n = (n+1)^2$.

For $n=5$: $T_5 = (5+1)^2 = 6^2 = 36$
For $n=6$: $T_6 = (6+1)^2 = 7^2 = 49$
For $n=7$: $T_7 = (7+1)^2 = 8^2 = 64$
The next 3 terms are $\boxed{\text{36, 49, 64}}$.

The difference between consecutive terms is constant: $7-3=4$, $11-7=4$, $15-11=4$. This is an arithmetic sequence with a first term $a=3$ and a common difference $d=4$. The $n$-th term is $T_n = a + (n-1)d = 3 + (n-1)4 = 3 + 4n - 4 = 4n - 1$.

For $n=5$: $T_5 = 4(5) - 1 = 20 - 1 = 19$
For $n=6$: $T_6 = 4(6) - 1 = 24 - 1 = 23$
For $n=7$: $T_7 = 4(7) - 1 = 28 - 1 = 27$
The next 3 terms are $\boxed{\text{19, 23, 27}}$.

3a)

Given $f(x) = x + 2$, we need to find $f(3)$.

The value is $\boxed{5}$.

3b)

Given $f(x) = 9x$, we need to find $f(5)$.

The value is $\boxed{45}$.

3c)

Given $f(x) = 9 - x$, we need to find $f(4)$.

The value is $\boxed{5}$.