Calculate the next three terms in each number sequence. a) 6; 14; 22; 30; ... b) 1; 2; 4; 8; 16; ... c) 64; 49; 36; 25; ... d) 729; 243; 81; ... e) 1; 1/2; 1/4; 1/8; ...

Pattern 1: A $1 \times 1$ red tile surrounded by white tiles, forming a $3 \times 3$ square.
Pattern 2: A $2 \times 2$ red tile square surrounded by white tiles, forming a $4 \times 4$ square.
Pattern 3: A $3 \times 3$ red tile square surrounded by white tiles, forming a $5 \times 5$ square.

The pattern shows that for pattern $n$, there is an $n \times n$ square of red tiles, and the total square (red and white tiles) is $(n+2) \times (n+2)$.

For Pattern 4, there will be a $4 \times 4$ square of red tiles, surrounded by white tiles, forming a $6 \times 6$ square in total.

⬜⬜⬜⬜⬜⬜
⬜🟥🟥🟥🟥⬜
⬜🟥🟥🟥🟥⬜
⬜🟥🟥🟥🟥⬜
⬜🟥🟥🟥🟥⬜
⬜⬜⬜⬜⬜⬜

(Here, ⬜ represents a white tile and 🟥 represents a red tile.)

For Pattern $n$:
Number of red tiles = $n^2$
Total tiles = $(n+2)^2$
Number of white tiles = Total tiles - Number of red tiles = $(n+2)^2 - n^2$

Pattern 1:
Red tiles = $1^2 = 1$
White tiles = $(1+2)^2 - 1^2 = 3^2 - 1 = 9 - 1 = 8$

Pattern 2:
Red tiles = $2^2 = 4$
White tiles = $(2+2)^2 - 2^2 = 4^2 - 4 = 16 - 4 = 12$

Pattern 3:
Red tiles = $3^2 = 9$
White tiles = $(3+2)^2 - 3^2 = 5^2 - 9 = 25 - 9 = 16$

Pattern 4:
Red tiles = $4^2 = 16$
White tiles = $(4+2)^2 - 4^2 = 6^2 - 16 = 36 - 16 = 20$

Pattern 5:
Red tiles = $5^2 = 25$
White tiles = $(5+2)^2 - 5^2 = 7^2 - 25 = 49 - 25 = 24$

Pattern 10:
Red tiles = $10^2 = 100$
White tiles = $(10+2)^2 - 10^2 = 12^2 - 100 = 144 - 100 = 44$

The number of red tiles in pattern $n$ is $n$ squared.
Rule for Red Tiles: $\text{Red tiles} = n^2$.

The number of white tiles increases by 4 for each subsequent pattern.
Alternatively, the number of white tiles in pattern $n$ can be found using the formula:
$\text{White tiles} = (n+2)^2 - n^2 = (n^2 + 4n + 4) - n^2 = 4n + 4$.

Rule for White Tiles: $\text{White tiles} = 4n + 4$.

The sequence is 9, 14, 19, 24, ...
The difference between consecutive terms is:
$14 - 9 = 5$
$19 - 14 = 5$
$24 - 19 = 5$
The common difference is 5. This is an arithmetic sequence.

The formula for the $n$-th term of an arithmetic sequence is $T_n = a + (n-1)d$, where $a$ is the first term and $d$ is the common difference.
Here, $a = 9$ and $d = 5$.

The rule is $\boxed{T_n = 5n + 4}$.

Substitute $n=20$ into the rule:

The 20th term is $\boxed{104}$.