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Find at least three different sequences beginning with the terms 1, 2, 4, whose terms are generated by a simple rule/formula. a. List down the first 8 terms. b. Define the rule/formula.

Find at least three different sequences beginning with the terms 1, 2, 4, whose terms are generated by a simple rule/formula. a. List down the first 8 terms. b. Define the rule/formula.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Find at least three different sequences beginning with the terms 1, 2, 4, whose terms are generated by a simple rule/formula. a. List down the first 8 terms. b. Define the rule/formula. For each of the following sequences, find a recurrence relation satisfied by this sequence. a. a = 2n + 3 12 b. a n 12 C. a = n + (-1)" 12 d. a = 5" n Suppose that the number of bacteria in a colony triples every hour. a. If 100 bacteria are used to begin a new colony, how many bacteria will be in the colony after 10 hours? b. Set up a recurrence relation for the number of bacteria after n hours. A factory makes custom sports cars at an increasing rate. In the first month, only one car is made, in the second month two cars are made, and so on, with n cars made in the nth month. a. Set up a recurrence relation for the number of cars produced in the first n months by this factory. b. How many cars are produced in the first year? c. Find an explicit formula for the number of cars produced in the first n months by this factory.
Transcribed Image Text:Find at least three different sequences beginning with the terms 1, 2, 4, whose terms are generated by a simple rule/formula. a. List down the first 8 terms. b. Define the rule/formula. For each of the following sequences, find a recurrence relation satisfied by this sequence. a. a = 2n + 3 12 b. a n 12 C. a = n + (-1)" 12 d. a = 5" n Suppose that the number of bacteria in a colony triples every hour. a. If 100 bacteria are used to begin a new colony, how many bacteria will be in the colony after 10 hours? b. Set up a recurrence relation for the number of bacteria after n hours. A factory makes custom sports cars at an increasing rate. In the first month, only one car is made, in the second month two cars are made, and so on, with n cars made in the nth month. a. Set up a recurrence relation for the number of cars produced in the first n months by this factory. b. How many cars are produced in the first year? c. Find an explicit formula for the number of cars produced in the first n months by this factory.
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