MathDB

Let

\{ a_n \}_{n=0}^{11}

and

\{ b_n \}_{n=0}^{11}

be sequences of real numbers. Suppose

a_0 = b_0 = -1

a_1 = b_1

, and for all integers

n \in \{2, 3, \ldots, 11\}

, \begin{align*} a_n & = a_{n-1} - (11 - n)^2(1 - (11 - (n - 1))^2)a_{n-2} \text{and} \\ b_n & = b_{n-1} - (12 - n)^2(1 - (12 - (n - 1))^2)b_{n-2}. \end{align*} If

b_{11} = 2a_{11}

, then determine the value of

a_1

Problem Statement