Let the terms be \( a, ar, ar^2, ar^3, \ldots \) According to the given condition: \[ a = ar + ar^2 \] Dividing both sides by \( a \) (assuming \( a \neq 0 \)): \[ 1 = r + r^2 \Rightarrow r^2 + r - 1 = 0 \] Solving the quadratic equation: \[ r = \frac{-1 \pm \sqrt{1 + 4}}{2} = \frac{-1 \pm \sqrt{5}}{2} \] Since \( r \) is positive, we take the positive root: \[ r = \frac{\sqrt{5} -1}{2} \]