Think back to the magical candy machine at your neighborhood grocery store. Suppose that the first time a quarter is put into the machine 1 Skittle comes out. The second time, 5 Skittles, the third time 25 Skittles, the fourth time, 125 Skittles, etc. a. Find both a recursive and closed formula for how many Skittles the nth customer gets. Recursive formula: an = Closed formula: An b. Check your solution for the closed formula by solving the recurrence relation using the Characteristic Root technique.
Think back to the magical candy machine at your neighborhood grocery store. Suppose that the first time a quarter is put into the machine 1 Skittle comes out. The second time, 5 Skittles, the third time 25 Skittles, the fourth time, 125 Skittles, etc. a. Find both a recursive and closed formula for how many Skittles the nth customer gets. Recursive formula: an = Closed formula: An b. Check your solution for the closed formula by solving the recurrence relation using the Characteristic Root technique.
Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter6: Fractions
Section6.4: Least Common Denominators
Problem 13E
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Transcribed Image Text:**Candy Machine Problem**
Think back to the magical candy machine at your neighborhood grocery store. Suppose that the first time a quarter is put into the machine, 1 Skittle comes out. The second time, 5 Skittles, the third time 25 Skittles, the fourth time, 125 Skittles, etc.
a. Find both a recursive and closed formula for how many Skittles the nth customer gets.
- **Recursive formula:** \( a_n = \)
- **Closed formula:** \( a_n = \)
b. Check your solution for the closed formula by solving the recurrence relation using the Characteristic Root technique.
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