That's Too Many Terms To Write!

Algebra Level 1

Consider an arithmetic progression whose first term and common difference are both 100. If the \(n^\text{th}\) term of this progression is equal to \(100!\), find \(n.\)

\[\]Notation: \(!\) denotes the factorial notation. For example, \(8! = 1\times2\times3\times\cdots\times8 \).