These sequences are extensively discussed in the notes and in the Wade textbook (5th ed.). Please refer to the following sections and exercises from the textbook to illustrate this type of synthetic problem.
Chapter 9: Section 9–7B. See solved problem 9–2, and problem 9–8.
Chapter 10: Section 10–9. See solved problem 10–2, and problems 10–13 through 10–15.
In addition, work as many related problems as possible from the end of the chapters, such as problem 10–39.