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21 Mar 2016, 04:29
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E
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Difficulty:
55%
(hard)
Question Stats:
61% (02:06) correct
39%
(02:27)
wrong
based on 179
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There is a sequence ni such, in which i is a positive integer, \(n_{i+1}=2n_i\). If \(n_1=1\), \(n_2=2\), \(n_3=4\), \(n_4=8\), what is the scope including \(n_{21}\)?
A. 100~1,000
B. 1,000~10,000
C. 10,000~100,000
D. 100,000~1,000,000
E. 1,000,000~
A. 100~1,000
B. 1,000~10,000
C. 10,000~100,000
D. 100,000~1,000,000
E. 1,000,000~
21 Mar 2016, 06:59
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n(i) = 2^(i - 1)
n(21) = 2^(21 - 1) = 2^20
2^10= 1024 = 10^3
2^20 > 10^3 * 10^3
2^20 > 10^6
Answer: E
n(21) = 2^(21 - 1) = 2^20
2^10= 1024 = 10^3
2^20 > 10^3 * 10^3
2^20 > 10^6
Answer: E
22 Mar 2016, 18:01
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There is a sequence ni such, in which i is a positive integer, ni+1=2ni.
If n1=1, n2=2, n3=4, n4=8, what is the scope including n21?
A. 100~1,000
B. 1,000~10,000
C. 10,000~100,000
D. 100,000~1,000,000
E. 1,000,000~
-> ni=2^(i-1) -> 2^10=1,024>1,000=10^3 -> n21=2^20=(2^10)^2>(10^3)^2=10^6
Thus, the answer is E.
If n1=1, n2=2, n3=4, n4=8, what is the scope including n21?
A. 100~1,000
B. 1,000~10,000
C. 10,000~100,000
D. 100,000~1,000,000
E. 1,000,000~
-> ni=2^(i-1) -> 2^10=1,024>1,000=10^3 -> n21=2^20=(2^10)^2>(10^3)^2=10^6
Thus, the answer is E.
