A sequence is defined by the formula $a_n=n^2-1$ for $1\le n\le 5$. List all the terms of this sequence.

Write an explicit formula for the arithmetic sequence whose first term is $a_1=-\frac{1}{2}$ and whose common difference is $d=\frac{1}{4}$.

Consider the sequence defined by $a_n=(-1{)}^n\cdot \frac{n^2}{2^n}$ for $n\ge 1$. Which classification best describes the behavior and properties of this sequence?

Simplify the explicit formula $a_n=3+(-2)\cdot (n-1)$ into standard linear form.

Two arithmetic sequences are given by $a_n=6+4(n-1)$ and $b_n=2+6(n-1)$. Find the smallest positive integer $n$ such that $a_n=b_n$.

Find the first $n$ for which the arithmetic sequence with $a_1=50$ and $d=-7$ becomes nonpositive $(a_n\le 0)$.

Which explanation correctly justifies why $0!=1$ using the recursive identity $n!=n\cdot (n-1)!$?

Simplify $\frac{(n+2)!}{n!}$ for a positive integer $n$. Express your answer in the simplest multiplicative form.

Compute $\frac{12!}{10!}$ by choosing the most efficient strategy.

The sequence $2,4,8,16,...$ is best classified as:

Compute the $10$^th term of the geometric sequence with $a_1=81$ and $r=-\frac{1}{3}$.

A student claims the sequence given by $s_n=5\cdot 2^n$ is geometric with common ratio $r=2$ and first term $a_1=5$. Evaluate the correctness of that claim with respect to the standard $a_n=a_1\cdot r^{n-1}$ indexing, and if needed, provide the correct $a_1$ for the student's formula or rewrite $s_n$ to match the standard form.