1a. Consider the sequence {?? }n≥0 which starts
1,2,7,20,61,122,..., defined by the recurrence relation ?? = 2??−1
+ 3??−2 and initial conditions ?0 = 1, ?1 = 2. Solve the recurrence
relation. That is, find a closed formula for ??. Show your
work.
The abandoned field behind your house is home to a large prairie
dog colony. Each week the size of the colony triples. However,
sadly 4 prairie dogs die each week as well (after the tripling
occurs). Consider...