NIMCET 2013 — Mathematics PYQ

Step 1: Set up the equation

Let the GP be $a,ar,a{r}^2,\dots$ where a > 0 and r > 0.

According to the problem:

Step 2: Simplify the equation

Divide both sides by $a{r}^{n-1}$ (since $a$ and $r$ are positive):

Step 3: Solve for $r$ using the quadratic formula

For $a{x}^2+bx+c=0$, $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$.

Step 4: Select the valid term

Since the problem states the terms are positive, the common ratio $r$ must be positive.

Correct Option: 4. $\frac{\sqrt{5}-1}{2}$