Question

Let the sequence $1, 2, 2, 4, 4, 4, 4, 8, 8, 8, 8, 8, 8, 8, 8, ...$ where n consecutive terms have the value n, then 1025th term is

• A. $2^9$
• B. $2^{10}$
• C. $2^{11}$
• D. $2^{8}$

Answer 1

Answer: (B)

Let the $1025 th $ term $= 2^{n} $
Then $1+2+4+8+.....+2^{n-1} < 1025 $
$\le 1+2+4+8+.....+2^{n}
\therefore 2^{n}-1 <1025 <2^{n+1} -1 $
or $2^{n} < 1026<2^{n+1} $
$ \Rightarrow n= 10$
$ \therefore $ reqd. term $= 2^{10}$