Question

In a GP of alternately positive and negative terms, any term is the AM of the next two terms. Then the common ratio is

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

Answer 1

The correct option is C $-2$

$\because$ The GP is of alternately positive and negative terms

$r<0$
Given $2a{r}^m=a{r}^{m+1}+a{r}^{m+2}$

$\Rightarrow 2=r+r^2(\because a,r\ne 0)$

$\Rightarrow r^2+r-2=0$

$\Rightarrow r=-2,1$

$\therefore r=-2(\because r<0)$