The smallest possible integer \(n\) such that \[1-2+3-4+5-6+\cdots +(-1)^{n+1}n \geq 100\] is

\(99\),

\(101\),

\(199\),

\(300\).

What is the sum of the terms of the sequence when \(n=1\)?

What about when \(n=2\)? \(n=3\)? \(n=4\)?

When will this sum reach \(100\)?

Or… what is the sum of the first \(2n\) terms of the sequence?