Question

If p(n) = ${10}^n+3\times 4^{n+1}+p$ is divisible by 3 for all values of n $\in$ N. Then find the least positive value of p for which p(n) is true.

• A. 1
• B. 2
• C. 5
• D. 3

Answer 1

The correct option is B 2

Since p(n) = ${10}^n+3\times 4^{n+1}+p$ is divisible by 3 for all values of n $\in$ N, this implies that it is true for n = 1.
$Now,{10}^1+3\times 4^{1+1}+p=58+p$
Nearest value of 58 + p to be divisible by 3 and for which p is positive is 60.
Therefore, p = 2.