Consider the honeycomb patterns below, which have side length $1,2$and $3$ hexagons respectively.

Find the side length of the first pattern that contains over $1000$ hexagons.

Find the first five terms of the following sequence:

$u_n=4n-1$ for $n\ge 1$

Find the first five terms of the following sequence:

$u_n=6n^2+2$ for $n\ge 1$

Find the first five terms of the following sequence:

$u_n=10-\frac{1}{4}{n}^2$ for $n\ge 1$

Find the first five terms of the following sequence:

$u_n=2^n-2$ for $n\ge 1$

Find the first five terms of the following sequence:

$u_n=(n+4)(n-3)$ for $n\ge 1$

Find the first five terms of the following sequence:

$u_n=4n-5$ for $n\ge 0$

Find the first five terms of the following sequence:

$u_n=\frac{25}{24}{n}^4-\frac{155}{12}{n}^3+\frac{1307}{24}{n}^2-\frac{1051}{12}n+45$ for $n\ge 0$

Find the tenth term of the sequence given by $u_n=5n-3$ for $n\ge 1$.