Question

Suppose you have the following recursion formula a1 = 1, a2 = 2, and an = a(n - 1)+ a(n - 2) for integers n ≥ 3. How would you determine the next three terms?

Answer 1

`\left\{\begin{array}{ccc}a_1=1\\a_2=2\\a_n=a_(n-1)+a_(n-2)&for\ n\geq3\end{array}\right\\\\a_3=a_(3-1)+a_(3-2)=a_2+a_1\to a_3=2+1=3\\\\a_4=a_(4-1)+a_(4-2)=a_3+a_2\to a_4=3+2=5\\\\a_5=a_(5-1)+a_(5-2)=a_4+a_3\to a_5=5+3=8\\\vdots`