Can the following Lemma be proved?

Lemma (Rokach-Goldstein)

Let x be a Generlized Fibonacci Sequence of positive integer numbers, x0 , x1 , x2 … such that for every I >=2 , xi = xi-1 +xi-2 , and x0 , x1 are co-prime to each other.

In this case , there exists some x , such that x is co prime to the sum of all numbers in the sequence.