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 (wedon’t count 0 in the alternating part).(a) Can you find a sequence of this type that starts with 5 elements that alternate sign?With 10 elements that alternate sign? Can you find a sequence with any number ofelements that alternate sign?(b) Given a particular starting integer, what negative number should you choose to makethe alternating part of the sequence as long as possible? For example, if your sequencestarted with 8, what negative number would give the longest alternating part? What ifyou started with 10? With n?