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 given sequence is equivalent to
$$ 1 + 2(2) + 4(2^{2}) + 8(2^{3}) + 16(2^{4}) + \ldots $$
$$ = 1 + (2^{2})^{1} + (2^{2})^{2} + (2^{3})^{3} + \ldots + (2^{2})^{k-1} + \ldots $$
Now, since this is a geometric series, we may solve  
$$ s_{k} = \frac{a(1 - r^{k})}{1-r} = \frac{1(1-4^{k})}{1-4} = 1025 $$
which easily can be shown to give $ 5 < k < 6$.
Hence, the integer $k$ we seek is $5$; and so, the $1025th$ term of the sequence is $4^{k} = 4^{5} = 1024.$
