Which sequence grows the SLOWEST for large nnn?
Fibonacci: Fn=Fn−1+Fn−2F_n = F_{n-1} + F_{n-2}Fn=Fn−1+Fn−2 (dominant root ϕ≈1.618\phi \approx 1.618ϕ≈1.618)
an=2an−1−0.5an−2a_n = 2a_{n-1} - 0.5a_{n-2}an=2an−1−0.5an−2 (dominant root ≈2\approx 2≈2)
bn=1.5bn−1+0.3bn−2b_n = 1.5b_{n-1} + 0.3b_{n-2}bn=1.5bn−1+0.3bn−2 (dominant root ≈1.53\approx 1.53≈1.53)
cn=cn−1+0.5cn−2c_n = c_{n-1} + 0.5c_{n-2}cn=cn−1+0.5cn−2 (dominant root ≈1.37\approx 1.37≈1.37)