Question

Write a rule that generates the Fibonacci sequence.

Answer 1

`\large\boxed{F_1=1,\ F_2=1}\\\boxed{F_n=F_(n-1)+F_(n-2),\qquad n\geq3}`

Explanation:

`\text{The Fibonacci sequence:}\\\\1,\ 1,\ 2,\ 3,\ 5,\ 8,\ 13,\ 21,\ 34,\ 55,\ ....\\\\F_1=1\\F_2=1\\F_3=F_2+F_1\to F_3=1+1=2\\F_4=F_3+F_2\to F_4=2+1=3\\F_5=F_4+F_3\to F_5=3+2=5\\F_6=F_5+F_4\to F_6=5+3=8\\F_7=F_6+F_5\to F_7=8+5=13\\F_8=F_7+F_6\to F_8=13+8=21\\\vdots\\F_n=F_(n-1)+F_(n-2)`