Explanation

(d)
Let $P(n) = 5^{2n + 2} - 24n - 25$
For $\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ n = 1$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ P(1) = 5^{4} - 24 - 25 = 576$
$\ \ \ \ \ \ \ \ \ \ P(2) = 5^{6} - 24(2) - 25 = 15552$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = 576 \times 27$
Here, we see that $P(n)$ is divisible by 576