Question 158
The Fibonacci sequence is the list of numbers that begins $1$, $2$, $3$, $5$, $8$, $13$ and continues with each subsequent number being the sum of the previous two.
Prove that when the first $n$ elements of the Fibonacci sequence are alternately added and subtracted, the result is an element of the sequence or the negative of an element of the sequence. For example,
$$
1-2+3-5=-3
$$
and $3$ is an element of the Fibonacci sequence.
Prove that when the first $n$ elements of the Fibonacci sequence are alternately added and subtracted, the result is an element of the sequence or the negative of an element of the sequence. For example,
$$
1-2+3-5=-3
$$
and $3$ is an element of the Fibonacci sequence.