Fibonacci Recurrence

This recurrence defines the Fibonacci sequence by saying that each new term is built from the two previous terms. The rule works because it captures a simple “growth by accumulation” pattern: once the first two starting values are chosen, every later value is forced by adding the last two. In the standard Fibonacci sequence, this produces numbers that rise slowly at first and then grow more quickly.

Use this formula when you need to generate or identify Fibonacci numbers from earlier terms. It also appears in problems about recursive patterns, combinatorics, and models where a quantity depends on the two previous stages.

• Adding only the immediately previous term instead of the previous two
• Starting from the wrong initial values and getting a different sequence
• Mixing up the index order, such as using F_{n+1} = F_n + F_{n-1} without checking the given terms