Let and be two sequences and for any positive integer

MATHEMATICS · Single correct · IB Diploma Programme · Mathematics: Applications and Interpretation · Number and Algebra · Number and Algebra

Problem

Let

\langle u_n \rangle

and

\langle v_n \rangle

be two sequences and for any positive integer

n

u_{n+1} = u_n - v_n

and

v_{n+1} = u_n + v_n

. If

u_{2024} = 2^{1012}

and

v_{2024} = 2^{1013}

, then

(v_1 + 2u_1)

is equal to. (A) 1 (B) 3 (C) 5 (D) 0.