Question

The two sequence of number $1,4,16,64,.......$ and $3,12,48,192,........$ are mixed as follows:$1,3,4,12,16,48,64,192,.......$. one of the numbers in the mixed in the mixed series is $1048576$, then number immediately preceding is-

• A. ${3.4}^9$
• B. ${3.4}^{10}$
• C. $4^9$
• D. $4^{10}$

Answer 1

The correct option is A ${3.4}^9$

$1,4,16,64,....\equiv 1,4,4^2,4^3,..\equiv 4^{n-1}$

$3,12,48,192,...\equiv 3\times 1,3\times 4,3\times 4^2,3\times 4^3...\equiv 3\times 4^{n-1}$

$1,3,4,12,16,48,64,192,..\equiv 1,3\times 1,4,3\times 4,4^2,3\times 4^2,4^3,3\times 4^3,..$

$1048576=4^{10}is{4}^{11-1}$

Number preceding $3\times 4^{10-1}={3.4}^9$