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anonymous
 one year ago
The following function defines a recursive sequence:
f(0) = 3
f(1) = 6
f(n) = 2•f(n 1)  f(n  2); for n > 1
Which of the following sequences is defined by this recursive function?
anonymous
 one year ago
The following function defines a recursive sequence: f(0) = 3 f(1) = 6 f(n) = 2•f(n 1)  f(n  2); for n > 1 Which of the following sequences is defined by this recursive function?

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.03, 6, 9, 12, … 3, 20, 95, 480, … 3, 6, 9, 12, … 3, 20, 95, 480, …

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1I will change my notations to \(a_{n}\) if you don't mind, ok?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1But you are given the first two terms \(a_0\) and \(a_1\) so just based on that you can exclude the rest of the options

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1u have only 2 possible options after doing elimination, right? and they are A and C

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1\(\large\color{black}{ \displaystyle a_n=2\cdot \left(a_{n1}\right) \left(a_{n2}\right) }\) \(\large\color{black}{ \displaystyle a_2=2\cdot \left(a_{21}\right) \left(a_{22}\right) }\) \(\large\color{black}{ \displaystyle a_2=2\cdot \left(a_{1}\right) \left(a_{0}\right) }\) \(\large\color{black}{ \displaystyle a_2=2\cdot \left(6\right) \left(3\right) }\) \(\large\color{black}{ \displaystyle a_2=12 +3 }\) \(\large\color{black}{ \displaystyle a_2=9}\)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1then, you can find \(a_3\) using the same formula

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1let me see.... \(\large\color{black}{ \displaystyle a_3=2\cdot \left(a_{31}\right) \left(a_{32}\right) }\) \(\large\color{black}{ \displaystyle a_2=2\cdot \left(a_{2}\right) \left(a_{1}\right)=2\cdot(9)(6)=186=12 }\)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1you can deduce that by logic, that you have a negative term \(a_{n1}\) (in this case a negative term \(a_{2}\) (which is =9) > so when multiplied times 2 it becomes twice as much and positive. This negative term \(a_2\) has a greater absolute value (or greater magnitude) than \(a_{n2}\) (and \(a_{n2}\) in this case is \(a_1\) which is 6) So you are having a case \(a_3=2\times ({\rm greater})~~({\rm smaller})~~~~~~~\Rightarrow~\rm positive\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0okay great thank you so much for your help! : )

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1and you know that it is 12 and 12, having eliminated every option besides A and C. And since the result (for \(a_2\)) must be positive, therefore it is 12 (not 12), and thus the answer is C.

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1this is kidnd of an implicit.... yw
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