Question

Find number of digits ${1025}^{th}$ term of the sequence $1,2,2,4,4,4,4,8,8,8,8,8,8,8,8,.........$

Answer 1

The given sequence is $1,2,2,4,4,4,4,8,8,\mathrm{8.....}$

$1$ comes one times.

$2$ comes two times.

$4$ comes four times

$8$ comes eight times

Let $x$ comes at ${1025}^{th}$ term

$1+2+4+\mathrm{8.....}x\ge 1025$

$\therefore$ The above sequence is $C.P$

$\therefore \frac{1(2^n-1)}{2-1}\ge 1025$

$\therefore 2^n-1\ge 1025(n=x)$

$\therefore 2^n\le 1026$

We have to find test $n$

$\therefore n=11$ .........$(2^{11}=2048)$

$(2^{10}=1024)$

$\therefore {1025}^{th}term$ = $2^{11}=2048$

$\therefore$ numbers of digit $=4$