Lastly, one other pattern seen within the Fibonacci sequence is displayed in Fig. 6. The Fibonacci sequence creates a palindrome, which is a word, phrase, number, or other sequence of characters which reads the same backward as it does forward. We can see in the figure that the Fibonacci sequence is generated backwards with alternating signs and we can generate this in general by adding the two previous terms together. More formally, we can use the equation \(x_n=-f_{n-1}+f_{n-2}.\)
To see how this formula works, let's calculate for \(n=-4\) to see the given solution for \(x_{n.}\) Notice that