Question

The terms of a G.P. are positive. If each term is equal to the sum of two terms that follow it, then the common ratio is

• A.
• B.
• C. 1

Answer 1

The correct option is A

Under condition $T_n$ = $T_{n+1}+T_{n+2}$

$\Rightarrow a{r}^{n-1}$ = $a{r}^n+a{r}^{n+1}\Rightarrow r^{n-1}$ = $r^n(1+r)$

$\Rightarrow r^2+r-1$ = 0 $\Rightarrow r$ = $\frac{-1\pm \sqrt{1+4}}{2}$= $\frac{-1\pm \sqrt{5}}{2}$

Since, each term is +ve.

Hence common ratio is $\frac{\sqrt{5}-1}{2}$