csat-suneung 2026 Q16

csat-suneung · South-Korea · csat__math 3 marks Sequences and series, recurrence and convergence Direct term computation from recurrence
The sequence $\left\{ a _ { n } \right\}$ has $a _ { 1 } = 1$ and satisfies $$a _ { n + 1 } = n ^ { 2 } a _ { n } + 1$$ for all natural numbers $n$. Find the value of $a _ { 3 }$. [3 points]
The sequence $\left\{ a _ { n } \right\}$ has $a _ { 1 } = 1$ and satisfies
$$a _ { n + 1 } = n ^ { 2 } a _ { n } + 1$$
for all natural numbers $n$. Find the value of $a _ { 3 }$. [3 points]