Question

Члены последовательности вычисляются по формуле Fk = Fk-1 + Fk-2.Чему равен F3, если F7 = 2 и F11 = 7?

Answer 1

F(11) = F(10) + F(9) = F(9) + F(8) + F(8) + F(7) = F(8) + F(7) + F(8) + F(8) + F(7) = 3F(8) + 2F(7)
7 = 3F(8) + 4 => F(8) = 1.

F(8) = F(7) + F(6) <=> F(6) = F(8) - F(7) = 1 - 2 = -1.
F(7) = F(6) + F(5) <=> F(5) = F(7) - F(6) = 2 - (-1) = 3.
F(6) = F(5) + F(4) <=> F(4) = F(6) - F(5) = -1 - 3 = -4.
F(5) = F(4) + F(3) <=> F(3) = F(5) - F(4) = 3 - (-4) = 7.