to the recurrence relation, for ally 9. Think back to the magical candy machine at your nelgil cery store. Suppose that the first time a quarter is put into the machine 1 Skittle comes out. The second time, 4 Skittles, the third time 16 Skit tles, the fourth time 64 Skittles, etc. (a) Find both a recursive and closed formula for how many Skittles 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 a1, 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