Are you smarter than me?

It is given that for any term $a_n$ of a GM of ratio $r$ :

$a_n = a_{n+1} + n_{n+2}$

$\Rightarrow a_n = a_n (r + r^2) \quad \Rightarrow r + r^2 = 1 \quad \Rightarrow r^2 + r - 1 = 0$

$\Rightarrow r = \frac {-1+\sqrt{5}} {2} = 0.618033989 \approx \boxed {0.61}$

x=a, y=ar, z=ar^2, x=y+z, a=ar+ar^2, Solve the quadratic equation r^2+r-1=0, Taking only the positive root, r=0.61

PS: In what way was it a calculus question???