There is a sequence ni such, in which i is a positive intege

[Max@Math Revolution]

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~


* A solution will be posted in two days.

[ratanvk]

Ans E

[Max@Math Revolution]

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.