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Nusret Balcı TMUA Paper 1 · Q17

Paper 1Sequences & series

A sequence of real numbers v0,v1,v2,…v_0,v_1,v_2,\ldots is defined by v0=0v_0=0, v1=1v_1=1, and the linear recurrence relation:

vn+1=2 vn−vn−1for n≥1.v_{n+1}=\sqrt2\,v_n-v_{n-1}\qquad\text{for }n\ge1.

What is the value of v101v_{101}?

A−1-1
B00
C11
D−2-\sqrt2
E2\sqrt2
F1−21-\sqrt2
G2−1\sqrt2-1
H1+21+\sqrt2

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