Question

Consider the sequence $1,2,2,4,4,4,4,8,8,8,8,8,8,8,8,....$ and so on. Then $1025th$ terms will be

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

Answer 1

Answer: (C)

$2^{10}$

Since,

$1$ $\left(1term\right)$

$2,2$ $\left(2terms\right)$

$4,4,4,4$ $\left(4terms\right)$

$8,8,8,8,8,8,8,8$ $\left(8terms\right)$

.......

.......

$2^n,2^n,2^n,\dots \dots \left(2^{n}terms\right)$

Now, let us calculate how many terms are in this series.

$1+2+4+8\dots \dots .+2^n$

Since, this is a geometric progression whose sum $=2^n-1$

Now,

$2^n-1=1025-1$

$2^n=1024$

$2^{10}=1024$

Hence, ${1025}^{th}$ term will be $2^{10}=1024$ and this value will start from ${1023}^{th}$ term as per the pattern .