Sequences are among the oldest objects of mathematical investigation, having been studied for over 3,500 years. Arithmetic and geometric sequences appear in the Rhind papyrus, a mathematical text containing 85 problems copied around 1650 BC by Egyptian scribe Ahmes from an earlier work. When algebra became sufficiently developed in the 1500s, more complicated problems were solved by using sequences. In the modern world, sequences have many real-life applications, such as predicting world population prospects. Let's discuss the following old English children's rhyme from one of the Rhind papyrus texts: As I was going to St. Ives I met a man with seven wives Each wife had seven sacks Each sack had seven cats Each cat had seven kits [kittens] Kits, cats, sacks, wives How many were going to St. Ives?
• Assuming that the speaker and the cat fanciers met by traveling in opposite directions, what is the answer?
• How many kittens are being transported?
• Kits, cats, sacks, wives; how many? You are required to:
• Answer the above questions one by one. Explain if you can connect your answers to sequences in any way.
• Pick a real-life application using sequences, preferably from the financial applications, and state it in a few sentences.
• Describe in three sentences what your strategy will be to solve your application problem.