Question: 9. Think back to the magical candy machine at cery store. Suppose that the first time a quarter is put into the machine pro 1

9. Think back to the magical candy machine at cery store. Suppose that the first time a quarter is put into the machine pro 1 Skittle comes out. The second time, 4 Skittles, the third time 16 Skit no tles, the fourth time 64 Skittles, etc. in (a) Find both a recursive and closed formula for how many Skittles ti the nth customer gets. (b) Check your solution for the closed formula by solving the re- currence relation using the Characteristic Root technique. 10. Let an be the number of 1 x n tile designs you can make using 1 x 1 squares available in 4 colors and 1 x 2 dominoes available in 5 colors. (a) First, find a recurrence relation to describe the problem. Explain why the recurrence relation is correct (in the context of the problem). (b) Write out the first 6 terms of the sequence d1, a2, . ... (c) Solve the recurrence relation. That is, find a closed formula. 1. You have access to 1 x 1 tiles which come in 2 different colors and 1 x 2 tiles which come in 3 different colors. We want to figure out how many different 1 x n path designs we can make out of these tiles

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Problem 9 Magical Candy Machine Part a Recursive and Closed Formula for Skittles Given to the nth Customer Recursive Formula The number of Skittles the nth customer receives follows a pattern where ea... View full answer

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