Start with a positive integer, then choose a negative integer. We’ll use these two numbers togenerate a sequence using the following rule: create the next term in the sequence by addingthe previous two. For example, if we started with 6 and −5, we would get the sequence6, −5, 1, −4alternating part, −3, −7, −10, −17, −27, . . .| {z} which starts with 4 elements that alternate sign before the terms are all negative. If we startedwith 3 and −2, we would get the sequence3, −2, 1, −1alternating part, 0, −1, −1, −2, −3, . . .| {z} which also starts with 4 elements that alternate sign before the terms are all non-positive.
Can you find a sequence of this type that starts with 5 elements that alternate sign?