Question

Consider the sequence $1,2,2,4,4,4,4,8,8,8,8,8,8,8,8......$ The ${1025}^{th}$ term of this sequence is $2^n,$ then $n$ is equal to

Answer 1

$1,2,2,4,4,4,4,8,8,8,8,8,8,8,8,.....$
$1+2+4+8=15=2^n–1$
$1+2+4+8+16+.....512=1023$
i.e., ${1023}^{th}$ term is $512$ and ${1024}^{th}$ term is $1024.$
Also, ${1025}^{th}$ term is $1024.$
i.e., $2^{10}$