hb wrote:
In the sequence 1, 2, 2, …, \(a_n\), …, \(a_n = a_{n-1}* a_{n-2}\). The value of \(a_{13}\) is how many times the value of \(a_{11}\)?
(A) 2
(B) 2^3
(C) 2^32
(D) 2^64
(E) 2^89
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Source:
Veritas Prep; Book 04
Chapter: Homework
Topic: Algebra
Question: 93
Question: Page 226
Solution: PDF Page 17 of 18
Edition: Third
My Question: Please provide an explanation on how to arrive at the answer.
Asked: In the sequence 1, 2, 2, …, \(a_n\), …, \(a_n = a_{n-1}* a_{n-2}\). The value of \(a_{13}\) is how many times the value of \(a_{11}\)?
\(a_n = a_{n-1}* a_{n-2}\)
Sequence = \({1,2,2,4,2^3,2^5,2^8,2^13,2^21,2^34,2^55,2^89,2^144...}\)
\(a_{13} = 2^{144}\)
\(a_{11} = 2^{55}\)
\(a_{13} = a^{11} * 2^{144-55}\)
\(a_{13} = a^{11} * 2^{89}\)
IMO E
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Kinshook Chaturvedi
Email: kinshook.chaturvedi@gmail.com