### Determine the value of the jewels

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Case Study The Mystery of the Missing Coulomb

This week Patty Madeye is going to be investigating the theft of a rare Orange Tiger Coulomb (shown at the right), which is owned by Madame Levare, who lives in West Floflux.

Since the jewels are quite valuable, Madam Levare stores them in the vault at the jeweler's store, West FloFlux GemStone in downtown West FloFlux. Only certain lockboxes in the vault were touched - it seems that the thief knew exactly what he was looking for.

Task #1 - Patty's first task is to determine the value of the jewels. She talks to the jeweler who created them and he estimates the value of the jewels in 1985 (when they were purchased) at \$65,000. The value is thought to increase (appreciate) by \$1500 per year. If this is true, how much would the jewels be worth in 2010? Explain how you arrived at your answer.

Task #2 - Patty talks to the jeweler and discovers that he remembers the 4-digit combination to the main vault in the store by writing it down in summation form. Here's what he wrote:

The combination is written in summation form, but some of the notation is cut off from where the paper is ripped. You'll need to figure out the full equation so that Patty can get into the vault to investigate.

Task #3 - Patty notices a pattern in the numbers of the lockboxes that were touched during the robbery and says that she thinks that it's a mathematical sequence. The sequence is { 8, 15, 22, 29, ...}. Determine whether this is a sequence (as far as you can tell) and what type (arithmetic or geometric) it is. Justify your answer by stating the general term for the sequence. Assuming Patty is correct, can you identify two other lockboxes that might have been emptied using this sequence?

Task #4 - Patty asks you to find out more information about the Fibonacci sequence as background for this week's episode. Do some research on the Fibonacci numbers by consulting the Kaplan Library or the internet. Find two facts or interesting properties about this fascinating topic and write a 1 page essay describing what you have found. Possible approaches include:

- The origin of the Fibonacci sequence?
- What is the connection between the Fibonacci sequence and the golden ratio?
- Does the "golden string" ever repeat?

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