Q. $10^{n} + 3\left( 4^{n + 2} \right) + 5$ is divisible by $(n \in N)$
A) 7
B) 5
C) 9
D) 17
Explanation
(c)
For $n = 1,\ 10^{n} + 3 \bullet 4^{n + 2} + 5$
$= 10 + 3 \bullet 4^{3} + 5 = 207$ This is divisible by 9.
$\therefore$ By induction, the result is divisible by 9.
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.