Common Sequences.

\(1, 4, 9, 16, 25, \ldots\)

The square numbers. The sequence \((s_n)_{n \ge 1}\) has closed formula \(s_n = n^2\)

\(1, 3, 6, 10, 15, 21, \ldots\)

The triangular numbers. The sequence \((T_n)_{n \ge 1}\) has closed formula \(T_n = \frac{n(n+1)}{2}\text{.}\)

\(1, 2, 4, 8, 16, 32,\ldots\)

The powers of 2. The sequence \((a_n)_{n \ge 0}\) with closed formula \(a_n = 2^n\text{.}\)

\(1, 1, 2, 3, 5, 8, 13, \ldots\)

The Fibonacci numbers (or Fibonacci sequence), defined recursively by \(F_n = F_{n-1} + F_{n-2}\) with \(F_1 = F_2 = 1\text{.}\)