Question

For the sequence $1,2,2,4,4,4,4,8,8,8,8,8,8,8,8,\dots ,$ the ${1025}^{\text{th}}$ term is

• A. $2^9$
• B. $2^{10}$
• C. $2^{11}$
• D. $2^{12}$

Answer 1

The correct option is B $2^{10}$

From the given sequence, it can be observed that the $t_{2^n}^{\text{th}}$ term starts with $2^n$
since, $t_1=1=2^0$
$t_2,t_3=2^1$
$t_4,t_5,t_6,t_7=2^2$
$t_8,\dots ,t_{15}=2^3$
$t_{16},\dots ,t_{31}=2^4$
So, $t_{1024}^{\text{th}}$ term starts with $2^{10}=1024$
$\therefore t_{1025}=1024=2^{10}$