Question

Three number are in G.P. If we double the middle term we get an A.P. then the common ratio of the G.P. is $-$ .

• A. $2\pm \sqrt{3}$
• B. $3\pm \sqrt{2}$
• C. $3\pm \sqrt{5}$
• D. none of these

Answer 1

Answer: (A)

$2\pm \sqrt{3}$

Let numbers be $\frac{a}{r},a,ar$

Now AP will be $\frac{a}{r},2a,ar$

using the Arithmetic mean, we get $2\left(2a\right)=\frac{a}{r}+ar4=\frac{1}{r}+r1+r^2=4r{r}^2-4r+1=0r=\frac{4\pm \sqrt{16-4}}{2}=2\pm \sqrt{3}$