Question

In a non-zero G.P., if $T_{p-1}+T_{p+1}=3T_p,$ where $T_n$ denotes the $n^{th}$ term of the G.P., then the common ratio of the G.P. can be

• A. $\frac{1+\sqrt{5}}{2}$
• B. $\frac{1-\sqrt{5}}{2}$
• C. $\frac{5-\sqrt{3}}{2}$
• D. $\frac{3-\sqrt{5}}{2}$

Answer 1

The correct option is D $\frac{3-\sqrt{5}}{2}$

$T_{p-1}+T_{p+1}=3T_p\Rightarrow a{r}^{p-2}+a{r}^p=3a{r}^{p-1}\Rightarrow a{r}^{p-2}[r^2-3r+1]=0\Rightarrow r^2-3r+1=0\therefore r=\frac{3\pm \sqrt{5}}{2}$