A sequence has an = (-1)ⁿ⁺¹(2n + 1). Write its first five terms…

A sequence is a function on $1, 2, 3, \dots$: a formula gives $a_n$ directly, a recurrence builds each term from earlier ones. The partial sum is $S_n = a_1 + \dots + a_n$, with $a_1 = S_1$ and $a_n = S_n - S_{n-1}$ for $n \geq 2$.