Question

Using mathematical induction, the numbers \( a_{n} \) are defined by \( a_{0} = 1,\; a_{n+1} = 3n^{2} + n + a_{n}, \; (n \ge 0) \). Then, \( a_{n} \) is equal to

• A. $n^{3}+n^{2}+1$
• B. $n^{3}-n^{2}+1$
• C. $n^{3}-n^{2}$
• D. $n^{3}+n^{2}$

Hint:

To solve induction patterns quickly, calculate the first few terms and verify options.

Answer 1

The Correct Option is B