1 The following geometric patterns. A Geometric shape pattern. The number of units used to form the pattern are 1, 4, 9, 16, 25. Identify the next number in the sequence.

The next pattern (4th pattern) will have $10 + 3 = 13$ sticks.
The number of sticks needed is $\boxed{\text{13 sticks}}$.

b) The number of sticks increases by 3 for each additional square added to the pattern.

c) Step 1: Complete the table using the common difference of 3.

d) Step 1: Identify the first term ($a$) and common difference ($d$).
$a = 4$, $d = 3$.

For the 18th pattern ($n=18$):

The number of sticks needed for the 18th pattern is $\boxed{\text{55 sticks}}$.

e) Step 1: Use the formula for the $n$-th term of an arithmetic sequence, $T_n = a + (n-1)d$.
Substitute $a=4$ and $d=3$.

The algebraic rule is $\boxed{T_n = 3n + 1}$.

1.1.2 Geometric shape pattern

a) Step 1: Analyze the pattern of dots.
Pattern 1 has $4 \times 4 = 16$ dots.
Pattern 2 has $3 \times 3 = 9$ dots.
Pattern 3 has $2 \times 2 = 4$ dots.
Pattern 4 has $1 \times 1 = 1$ dot.

The side length of the square is $5-n$. So, $T_n = (5-n)^2$.

The number of dots in the 8th term is $\boxed{\text{9 dots}}$.

b) Step 1: Use the rule $T_n = (5-n)^2$ for the 10th term ($n=10$).

The 10th term of the pattern is $\boxed{\text{25 dots}}$.

c) Step 1: Based on the analysis in part (a), the algebraic rule is the square of $(5-n)$.
The algebraic rule is $\boxed{T_n = (5-n)^2}$.