If the sequence 1,2,2,4,4,4,4,8,8,8,8,8,8,8,8,….. where ‘n’ consecutive  terms has value ‘n’ then 1025th terms is a four digit number abcd, the matrix A is defined as $\left(\begin{array}{cc}a& b\\ c& d\end{array}\right)$ then the value of   $\frac{\left|adj\left(3A\right)\right|}{4}.$

Let m= number of times the digit n is repeated in the sequence.

m=1,2,4,8..... The sequence {m} is a GP

N th term of GP is 2^N-1

Sum of N terms = 2^N-1

$2^N-1\ge 1025$

Minimum m for which $2^N-1\ge 1025$ is 2048 or 2¹¹ which is 12 th term

1025 term is 11 th term in the sequence {m}(i.e)2¹⁰

$abcd=1024$