1025th term of the sequence $ 1,2,2,4,4,4,4,8,8,8,8,8,8,8,8, ... $ Consider the following sequence - $$ 1,2,2,4,4,4,4,8,8,8,8,8,8,8,8, ... $$
In this sequence, what will be the $ 1025^{th}\, term $
So, when we write down the sequence and then write the value of $ n $ (Here, $n$ stands for the number of the below term) above it  We can observe the following -

$1 - 1$
$2 - 2 $
$3 - 2$
$4 - 4$ 
$5 - 4$
. . .
$8 - 8$ 
$9 - 8$
. . .

We can notice that $ 4^{th}$ term is 4 and similarly, the $ 8^{th}$ term is 8.
So the $ 1025^{th}$ term must be 1024 as $ 1024^{th} $ term starts with 1024.
So the value of $ 1025^{th}$ term is $ 2^{10} $ . 
Is there any other method to solve this question?

A higher brow way of writing the same thing is to say the $n^{th}$ term is 
$2^{\lfloor \log_2 n\rfloor}$, then to evaluate that at $n=1025$.  The base $2$ log of $1025$ is slightly greater than $10$, so the term is $2^{10}=1024$.
