Question

Which of the following can also be written as a recursive sequence?

Select all that apply.

geometric sequence
arithmetic sequence
Fibonacci sequence
exponential sequence

Answer 1

All four.

Examples of recursive definitions:
- Arithmetic: a1 = a, a_{n+1} = a_n + d.
- Geometric: g1 = g, g_{n+1} = r·g_n.
- Fibonacci: F1 = 1, F2 = 1 (or F0 = 0, F1 = 1), F_{n+1} = F_n + F_{n-1}.
- Exponential (a_n = c·b^n, which is a geometric-type sequence): e1 = c·b, e_{n+1} = b·e_n.