Question 1: Write the next three numbers in each of the following sequences. Say whether each sequence is a constant difference or constant ratio sequence or neither.

$6-3=3$  
$9-6=3$  
$12-9=3$  
$15-12=3$  
The difference is constant (3). This is a constant difference sequence.

$15+3=18$  
$18+3=21$  
$21+3=24$  
The next three numbers are 18, 21, 24.  
The sequence is a constant difference sequence.
$$
\boxed{\text{18, 21, 24; Constant difference}}
$$

$\frac{4}{2}=2$  
$\frac{8}{4}=2$  
$\frac{16}{8}=2$  
The ratio is constant (2). This is a constant ratio sequence.

$16 \times 2=32$  
$32 \times 2=64$  
$64 \times 2=128$  
The next three numbers are 32, 64, 128.  
The sequence is a constant ratio sequence.
$$
\boxed{\text{32, 64, 128; Constant ratio}}
$$

$11-7=4$  
$15-11=4$  
$19-15=4$  
$23-19=4$  
The difference is constant (4). This is a constant difference sequence.

$23+4=27$  
$27+4=31$  
$31+4=35$  
The next three numbers are 27, 31, 35.  
The sequence is a constant difference sequence.
$$
\boxed{\text{27, 31, 35; Constant difference}}
$$

$4-1=3$  
$9-4=5$  
$16-9=7$  
The differences are not constant.

$\frac{4}{1}=4$  
$\frac{9}{4}=2.25$  
The ratios are not constant.

$5^2=25$  
$6^2=36$  
$7^2=49$  
The next three numbers are 25, 36, 49.  
The sequence is neither a constant difference nor a constant ratio sequence.
$$
\boxed{\text{25, 36, 49; Neither}}
$$

$36-18=18$  
$54-36=18$  
$72-54=18$  
The difference is constant (18). This is a constant difference sequence.

$72+18=90$  
$90+18=108$  
$108+18=126$  
The pattern is adding 18 to the previous term. The sequence is a constant difference sequence. The missing numbers are 90, 108, 126.
$$
\boxed{\text{Constant difference; 90, 108, 126}}
$$

$\frac{9}{3}=3$  
$\frac{27}{9}=3$  
The ratio is constant (3). This is a constant ratio sequence.

$27 \times 3=81$  
$81 \times 3=243$  
$243 \times 3=729$  
The pattern is multiplying the previous term by 3. The sequence is a constant ratio sequence. The missing numbers are 81, 243, 729.
$$
\boxed{\text{Constant ratio; 81, 243, 729}}
$$