When $n = 5$, the value of the expression $2n^2 + 1$ is 51.

Would you like more details or have any further questions? Here are five related questions to explore:

1. What is the value of $2n^2 + 1$ when $n = 3$?
2. Can you find a general formula for the sum of this sequence as $n$ increases?
3. How does the expression change if the coefficient of $n^2$ is altered?
4. What would be the result of $3n^2 + 1$ for $n = 5$?
5. Can you find the value of the derivative of $2n^2 + 1$?

Tip: For functions involving powers of $n$, analyzing the rate of change using derivatives can give deeper insights.