Problem
ALG-B3-M06-P001 Linear Recurrence
#1
★★☆☆☆ Level 2 of 5
Let \(f:\mathbb Z\to\mathbb Z\), \(f(0)=-1\), and \(f(n+1)=f(n)+4\). Find \(f(n)\).
Move forward and backward from zero.
For \(n>0\), induction gives \(f(n)=4n-1\). For \(n<0\), from \(f(n)=f(n+1)-4\) we get the same formula. The answer is \(f(n)=4n-1\).
Basic control of working on all of \(\mathbb Z\), including negatives.