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?

The first term is $2^0=1$; the next $2^1=2$ terms are equal to $2^1=2$; the next $2^2=4$ terms are equal to $4$ and so on. Since
$$
2^0+2^1+2^2+\dots+2^n=2^{n+1}-1
$$
the term at place $1023$ is $512$. The next $2^{10}$ terms are equal to $1024$.
