Question

Consider the sequence $1,2,2,4,4,4,4,8,8,8,8,8,8,8,8,...$

Then ${1025}^{\mathrm{th}}$ term is

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

Answer 1

The correct option is B

$2^{10}$

Explanation for correct answer.

Let $\mathrm{m}=\mathrm{Number}\mathrm{of}\mathrm{times}\mathrm{a}\mathrm{number}\mathrm{n}\mathrm{is}\mathrm{repeated}\mathrm{in}\mathrm{the}\mathrm{given}\mathrm{sequence}\left(\mathrm{n}\right)$

Given sequence $1,2,2,4,4,4,4,8,8,8,8,8,8,8,8,...$

By observing the sequence, $2^0=1$ is the first term.

$2^1=2$ (repeated $2$ times)

$2^2=4$ (repeated $4$ times)

$2^3=8$ (repeated $8$ times)

Next term will be $2^4=16$. It will be repeated $16$ times.

Since we double the number each time we know the pattern will go:

$1,2,4,8,16,32,64,128,256,512,1024...$

The number $1024$ will start on term $1024$, therefore the ${1025}^{\mathrm{th}}$ term will be $1024$.

$1024$$=2^{10}$

Hence option (B) is the answer.