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?

$$ 2^0 + 2^1 + 2^2 + 2^3 + ... + 2^n < 1025 = 2^{10}+ 2^0 $$
$$ 2^1 + 2^2 + 2^3 + ... + 2^n < 2^{10} $$
$$ \frac{1}{2^9} + \frac{1}{2^8} + ... + \frac{1}{2^{10-n}} < 1 $$
In the left-hand side of the above inequality, we've acquired a geometrical sequence. The summation formula for geometrical series is;
$$ S = \frac{a(1-r^n)}{1-r} $$
So this summation must be smaller than 1, with this condition stated we can set n = 9. 
$$ 2^0 + 2^1 + 2^2 + ... + 2^9 = 1023 $$
We are now able to conclude that the term at place 1024 and 1025 (at the same time) is 1024.
