A new clothing store wants to advertise to attract more customers. They decide the best way is to spread information about a special sale by telling it like a secret. The owner starts by telling one person about the sale on May 1. That person is responsible for telling one other person about the sale on each of the next two days (May 2 and May 3). So, on May 2, two people know about the sale. On May 3, the one person who heard about the sale on May 2 and the one person who heard it on May 1 must each tell one more person. Now, four people know about the sale. It is important for 1000 people to hear about the sale by May 15. Is this outcome likely to occur if each person who hears about the sale tells one other person the next day and the day after?
Extension: Choose two whole numbers (number one and number two). Add them together and form a Fibonacci-like sequence (add number one and number two together to get number three, then add number two and number three together to get number four, etc.). End with a total of ten numbers. Repeat the process by starting with two different numbers. Answer the following questions:What is the relationship between the seventh term and the sum of the terms (for each sequence)?
What is the relationship between the seventh term and the tenth term (for each sequence)? Explain.
Relevant InterMath Investigations:
Multiplying Rabbits : Examine how the family tree of a rabbit forms the Fibonacci sequence and the golden ratio.
Fibonacci Extended : Identify an explicit pattern between terms in a group of numbers that are generated recursively.